Question 1

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length
using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle.
Rationalize the denominator if applicable.
-Find  csc⁡A\csc \mathrm { A }cscA  when  b=16\mathrm { b } = 16b=16  and  c=34\mathrm { c } = 34c=34

Accepted Answer

A)    815\frac { 8 } { 15 }158​ 
B)    1715\frac { 17 } { 15 }1517​ 
C)    1517\frac { 15 } { 17 }1715​ 
D)    178\frac { 17 } { 8 }817​E) A) and B)
F) A) and C)

Question 2

Find all values of θ, if θ is in the interval [0, 360°)  and has the given function value.
- sec⁡θ\sec 	hetasecθ  is undefined

Accepted Answer

A)    90∘90 ^ { \circ }90∘ 
B)    90∘90 ^ { \circ }90∘  and  270∘270 ^ { \circ }270∘ 
C)    0∘0 ^ { \circ }0∘ 
D)    0∘0 ^ { \circ }0∘  and  180∘180 ^ { \circ }180∘E) A) and D)
F) C) and D)

Question 3

Solve the problem for the given information.
-Find the equation of a line passing through the origin so that the cosine of the angle between the line in quadrant  III  and the positive  xxx -axis is  32\frac { \sqrt { 3 } } { 2 }23​​ .

Accepted Answer

A)    y=32xy = \frac { \sqrt { 3 } } { 2 } xy=23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​x 
B)    y=33xy = \frac { \sqrt { 3 } } { 3 } xy=33c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​x 
C)    y=xy = xy=x 
D)    y=3xy = \sqrt { 3 } xy=3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​xE) C) and D)
F) None of the above

Question 4

Decide whether the statement is possible or impossible for an angle θ.
- cos⁡θ=511\cos 	heta = \frac { 5 } { 11 }cosθ=115​  and  sec⁡θ=115\sec 	heta = \frac { 11 } { 5 }secθ=511​

Accepted Answer

A)   Impossible
B)   Possible C) A) and B)
D) undefined

Question 5

Use the fundamental identities to find the value of the trigonometric function.
-Find  sec⁡θ\sec 	hetasecθ , given that  tan⁡θ=3.7320508	an 	heta = 3.7320508tanθ=3.7320508  and  θ	hetaθ  is in quadrant  III .

Accepted Answer

A)    −3.8637033- 3.8637033−3.8637033 
B)    −2.1753277- 2.1753277−2.1753277 
C)    2.17532772.17532772.1753277 
D)    3.86370333.86370333.8637033E) A) and C)
F) A) and B)

Question 6

Decide whether the statement is possible or impossible for an angle θ.
- tan⁡θ=−2.14	an 	heta = - 2.14tanθ=−2.14

Accepted Answer

A)   Possible
B)   Impossible C) A) and B)
D) undefined

Question 7

Use the fundamental identities to find the value of the trigonometric function.
-Find  cot⁡θ\cot 	hetacotθ , given that  cos⁡θ=2129\cos 	heta = \frac { 21 } { 29 }cosθ=2921​  and  θ	hetaθ  is in quadrant IV.

Accepted Answer

A)    −2124- \frac { 21 \sqrt { 2 } } { 4 }−4212c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
B)    −2120- \frac { 21 } { 20 }−2021​ 
C)    −2021- \frac { 20 } { 21 }−2120​ 
D)    2921\frac { 29 } { 21 }2129​E) All of the above
F) A) and C)

Question 8

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given
value is a decimal, round your answer to three decimal places.
- cot⁡θ\cot 	hetacotθ , given that  tan⁡θ=0.2352	an 	heta = 0.2352tanθ=0.2352

Accepted Answer

A)    4.2524.2524.252 
B)    4.2664.2664.266 
C)    4.2594.2594.259 
D)    4.2454.2454.245E) None of the above
F) A) and C)

Question 9

Without using a calculator, give the exact trigonometric function value with rational denominator.
- sec⁡45∘\sec 45 ^ { \circ }sec45∘

Accepted Answer

A)    233\frac { 2 \sqrt { 3 } } { 3 }323c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
B)   1
C)    12\frac { 1 } { 2 }21​ 
D)    2\sqrt { 2 }2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​E) C) and D)
F) A) and D)

Question 10

If r is a positive number and the point (x, y)  is in the indicated quadrant, decide whether the given ratio is positive or
negative.
-II,  xr\frac { x } { r }rx​

Accepted Answer

A)   Negative
B)   Positive C) A) and B)
D) undefined

Question 11

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure.
- sec⁡(−1∘) \sec \left( - 1 ^ { \circ } \right) sec(−1∘)   and  sin⁡(−1∘) \sin \left( - 1 ^ { \circ } \right) sin(−1∘)

Accepted Answer

A)   negative and negative
B)   positive and negative
C)   negative and positive
D)   positive and positive E) A) and B)
F) None of the above

Question 12

Use the fundamental identities to find the value of the trigonometric function.
-Find  sin⁡θ\sin 	hetasinθ , given that  cos⁡θ=49\cos 	heta = \frac { 4 } { 9 }cosθ=94​  and  θ	hetaθ  is in quadrant IV.

Accepted Answer

A)    −654- \frac { \sqrt { 65 } } { 4 }−465c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
B)    −65- \sqrt { 65 }−65c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    −94- \frac { 9 } { 4 }−49​ 
D)    −659- \frac { \sqrt { 65 } } { 9 }−965c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​E) C) and D)
F) B) and D)

Question 13

Find the exact value of the expression.
- cot⁡30∘\cot 30 ^ { \circ }cot30∘

Accepted Answer

A)   1
B)    32\frac { \sqrt { 3 } } { 2 }23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
C)    3\sqrt { 3 }3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)    33\frac { \sqrt { 3 } } { 3 }33c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​E) A) and B)
F) A) and C)

Question 14

Solve the problem.
-A  6.16.16.1 -ft fence is  10.738ft10.738 \mathrm { ft }10.738ft  away from a plant in the direction of the sun. It is observed that the shadow of the fence extends exactly to the bottom of the plant. (See drawing)  Find  θ	hetaθ , the angle of elevation of the sun at that time. Round the measure of the angle to the nearest tenth of a degree when necessary.

Accepted Answer

A)    θ=29.8∘	heta = 29.8 ^ { \circ }θ=29.8∘ 
B)    θ=29.6∘	heta = 29.6 ^ { \circ }θ=29.6∘ 
C)    θ=31∘	heta = 31 ^ { \circ }θ=31∘ 
D)    θ=29.4∘	heta = 29.4 ^ { \circ }θ=29.4∘E) A) and C)
F) None of the above

Question 15

Find the reference angle for the given angle.
- 109∘109 ^ { \circ }109∘

Accepted Answer

A)    81∘81 ^ { \circ }81∘ 
B)    29∘29 ^ { \circ }29∘ 
C)    19∘19 ^ { \circ }19∘ 
D)    71∘71 ^ { \circ }71∘E) All of the above
F) None of the above

Question 16

Solve the problem.
-Radio direction finders are set up at points  AAA  and  B,8.68miB , 8.68 \mathrm { mi }B,8.68mi  apart on an east-west line. From  AAA  it is found that the bearing of a signal from a transmitter is  N54.3∘E\mathrm { N } 54.3 ^ { \circ } \mathrm { E }N54.3∘E , while from  B\mathrm { B }B  it is  N35.7∘W\mathrm { N } 35.7 ^ { \circ } \mathrm { W }N35.7∘W . Find the distance of the transmitter from B, to the nearest hundredth of a mile.

Accepted Answer

A)    5.07mi5.07 \mathrm { mi }5.07mi 
B)    4.57mi4.57 \mathrm { mi }4.57mi 
C)    7.05mi7.05 \mathrm { mi }7.05mi 
D)    7.55mi7.55 \mathrm { mi }7.55miE) C) and D)
F) None of the above

Question 17

Use the fundamental identities to find the value of the trigonometric function.
-Find  cos⁡θ\cos 	hetacosθ , given that  tan⁡θ=−47	an 	heta = - \frac { 4 } { 7 }tanθ=−74​  and  θ	hetaθ  is in quadrant II.

Accepted Answer

A)    654\frac { \sqrt { 65 } } { 4 }465c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
B)    −76565- \frac { 7 \sqrt { 65 } } { 65 }−65765c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
C)    76565\frac { 7 \sqrt { 65 } } { 65 }65765c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
D)    −657- \frac { \sqrt { 65 } } { 7 }−765c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​E) A) and B)
F) None of the above

Question 18

If n is an integer, n ∙ 180° represents an integer multiple of 180°, and (2n + 1)  ∙ 90° represents an odd integer multiple of
90°. Decide whether the expression is equal to 0, 1, -1, or is undefined.
- cos⁡((2n+1) ⋅90∘) \cos \left( ( 2 n + 1 )  \cdot 90 ^ { \circ } \right) cos((2n+1) ⋅90∘)

Accepted Answer

A)   0
B)    −1- 1−1 
C)   Undefined
D)   1 E) C) and D)
F) None of the above

Question 19

Evaluate the expression.
- cot⁡(−90∘) \cot \left( - 90 ^ { \circ } \right) cot(−90∘)

Accepted Answer

A)    −1- 1−1 
B)    22\frac { \sqrt { 2 } } { 2 }22c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
C)   Undefined
D)   0 E) A) and B)
F) None of the above

Question 20

Sketch an angle  θ	hetaθ  in standard position such that  θ	hetaθ  has the least positive measure and the given point is on the terminal
side of  θ.	heta _ { . }θ.​ 
- (4,−2) ( 4 , - 2 ) (4,−2)

Accepted Answer

A)  
B)  
C)  
D)   E) B) and C)
F) A) and B)

Exam 5: Trigonometric Functions

Without using a calculator, give the exact trigonometric function value with rational denominator. - $\sec 45 ^ { \circ }$

Correct Answer
verified

Find the exact value of the expression. - $\cot 30 ^ { \circ }$

Correct Answer
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If n is an integer, n ∙ 180° represents an integer multiple of 180°, and (2n + 1) ∙ 90° represents an odd integer multiple of 90°. Decide whether the expression is equal to 0, 1, -1, or is undefined. - $\cos \left( ( 2 n + 1 ) \cdot 90 ^ { \circ } \right)$

Correct Answer
verified

Decide whether the statement is possible or impossible for an angle θ. - $\tan \theta = - 2.14$

Correct Answer
verified

Evaluate the expression. - $\cot \left( - 90 ^ { \circ } \right)$

Correct Answer
verified

Use the fundamental identities to find the value of the trigonometric function. -Find $\sin \theta$ , given that $\cos \theta = \frac { 4 } { 9 }$ and $\theta$ is in quadrant IV.

Correct Answer
verified

Use the fundamental identities to find the value of the trigonometric function. -Find $\sec \theta$ , given that $\tan \theta = 3.7320508$ and $\theta$ is in quadrant $I$ .

Correct Answer
verified

Correct Answer
verified

Find the reference angle for the given angle. - $109 ^ { \circ }$

Correct Answer
verified

If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or negative. -II, $\frac { x } { r }$

Correct Answer
verified

Use the fundamental identities to find the value of the trigonometric function. -Find $\cos \theta$ , given that $\tan \theta = - \frac { 4 } { 7 }$ and $\theta$ is in quadrant II.

Correct Answer
verified

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. - $\sec \left( - 1 ^ { \circ } \right)$ and $\sin \left( - 1 ^ { \circ } \right)$

Correct Answer
verified

Solve the problem for the given information. -Find the equation of a line passing through the origin so that the cosine of the angle between the line in quadrant $I$ and the positive $x$ -axis is $\frac { \sqrt { 3 } } { 2 }$ .

Correct Answer
verified

Correct Answer
verified

Decide whether the statement is possible or impossible for an angle θ. - $\cos \theta = \frac { 5 } { 11 }$ and $\sec \theta = \frac { 11 } { 5 }$

Correct Answer
verified

Correct Answer
verified

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value. - $\sec \theta$ is undefined

Correct Answer
verified

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given value is a decimal, round your answer to three decimal places. - $\cot \theta$ , given that $\tan \theta = 0.2352$

Correct Answer
verified

Correct Answer
verified

Use the fundamental identities to find the value of the trigonometric function. -Find $\cot \theta$ , given that $\cos \theta = \frac { 21 } { 29 }$ and $\theta$ is in quadrant IV.

Correct Answer
verified

Exam 5: Trigonometric Functions

Without using a calculator, give the exact trigonometric function value with rational denominator. - sec⁡45∘\sec 45 ^ { \circ }sec45∘

Correct AnswerverifiedShow Answer

Find the exact value of the expression. - cot⁡30∘\cot 30 ^ { \circ }cot30∘

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Decide whether the statement is possible or impossible for an angle θ. - tan⁡θ=−2.14\tan \theta = - 2.14tanθ=−2.14

Correct AnswerverifiedShow Answer

Evaluate the expression. - cot⁡(−90∘) \cot \left( - 90 ^ { \circ } \right) cot(−90∘)

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Use the fundamental identities to find the value of the trigonometric function. -Find sin⁡θ\sin \thetasinθ , given that cos⁡θ=49\cos \theta = \frac { 4 } { 9 }cosθ=94​ and θ\thetaθ is in quadrant IV.

Correct AnswerverifiedShow Answer

Use the fundamental identities to find the value of the trigonometric function. -Find sec⁡θ\sec \thetasecθ , given that tan⁡θ=3.7320508\tan \theta = 3.7320508tanθ=3.7320508 and θ\thetaθ is in quadrant III .

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Find the reference angle for the given angle. - 109∘109 ^ { \circ }109∘

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If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or negative. -II, xr\frac { x } { r }rx​

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Use the fundamental identities to find the value of the trigonometric function. -Find cos⁡θ\cos \thetacosθ , given that tan⁡θ=−47\tan \theta = - \frac { 4 } { 7 }tanθ=−74​ and θ\thetaθ is in quadrant II.

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Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. - sec⁡(−1∘) \sec \left( - 1 ^ { \circ } \right) sec(−1∘) and sin⁡(−1∘) \sin \left( - 1 ^ { \circ } \right) sin(−1∘)

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Solve the problem for the given information. -Find the equation of a line passing through the origin so that the cosine of the angle between the line in quadrant III and the positive xxx -axis is 32\frac { \sqrt { 3 } } { 2 }23​​ .

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Decide whether the statement is possible or impossible for an angle θ. - cos⁡θ=511\cos \theta = \frac { 5 } { 11 }cosθ=115​ and sec⁡θ=115\sec \theta = \frac { 11 } { 5 }secθ=511​

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Sketch an angle θ\thetaθ in standard position such that θ\thetaθ has the least positive measure and the given point is on the terminal side of θ.\theta _ { . }θ.​ - (4,−2) ( 4 , - 2 ) (4,−2)

Correct AnswerverifiedShow Answer

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value. - sec⁡θ\sec \thetasecθ is undefined

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Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given value is a decimal, round your answer to three decimal places. - cot⁡θ\cot \thetacotθ , given that tan⁡θ=0.2352\tan \theta = 0.2352tanθ=0.2352

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Use the fundamental identities to find the value of the trigonometric function. -Find cot⁡θ\cot \thetacotθ , given that cos⁡θ=2129\cos \theta = \frac { 21 } { 29 }cosθ=2921​ and θ\thetaθ is in quadrant IV.

Correct AnswerverifiedShow Answer

Without using a calculator, give the exact trigonometric function value with rational denominator. - $\sec 45 ^ { \circ }$

Correct Answer
verified

Find the exact value of the expression. - $\cot 30 ^ { \circ }$

Correct Answer
verified

Correct Answer
verified

Decide whether the statement is possible or impossible for an angle θ. - $\tan \theta = - 2.14$

Correct Answer
verified

Evaluate the expression. - $\cot \left( - 90 ^ { \circ } \right)$

Correct Answer
verified

Use the fundamental identities to find the value of the trigonometric function. -Find $\sin \theta$ , given that $\cos \theta = \frac { 4 } { 9 }$ and $\theta$ is in quadrant IV.

Correct Answer
verified

Use the fundamental identities to find the value of the trigonometric function. -Find $\sec \theta$ , given that $\tan \theta = 3.7320508$ and $\theta$ is in quadrant $I$ .

Correct Answer
verified

Correct Answer
verified

Find the reference angle for the given angle. - $109 ^ { \circ }$

Correct Answer
verified

If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or negative. -II, $\frac { x } { r }$

Correct Answer
verified

Use the fundamental identities to find the value of the trigonometric function. -Find $\cos \theta$ , given that $\tan \theta = - \frac { 4 } { 7 }$ and $\theta$ is in quadrant II.

Correct Answer
verified

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. - $\sec \left( - 1 ^ { \circ } \right)$ and $\sin \left( - 1 ^ { \circ } \right)$

Correct Answer
verified

Solve the problem for the given information. -Find the equation of a line passing through the origin so that the cosine of the angle between the line in quadrant $I$ and the positive $x$ -axis is $\frac { \sqrt { 3 } } { 2 }$ .

Correct Answer
verified

Correct Answer
verified

Decide whether the statement is possible or impossible for an angle θ. - $\cos \theta = \frac { 5 } { 11 }$ and $\sec \theta = \frac { 11 } { 5 }$

Correct Answer
verified

Correct Answer
verified

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value. - $\sec \theta$ is undefined

Correct Answer
verified

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given value is a decimal, round your answer to three decimal places. - $\cot \theta$ , given that $\tan \theta = 0.2352$

Correct Answer
verified

Correct Answer
verified

Use the fundamental identities to find the value of the trigonometric function. -Find $\cot \theta$ , given that $\cos \theta = \frac { 21 } { 29 }$ and $\theta$ is in quadrant IV.

Correct Answer
verified