Question 1

Use the properties of angle measures to find the measure of each marked angle.
-tan ϴ > 0 and sin ϴ < 0

Accepted Answer

A) Quadrant I 
B) Quadrant III 
C) Quadrant II 
D) Quadrant IV 
A) Quadrant I 
B) Quadrant III 
C) Quadrant II 
D) Quadrant IV B

Question 2

Use the fundamental identities to find the value of the trigonometric function.
-An alien observer on Planet X can approximate distances in the sky by using his "hand" at arm's length. An outstretched hand is about 35 arc degrees, a clenched fist is about 25 arc degrees, and a
Thumb corresponds to about 1 arc degree. (i)If one clenched fist plus one outstretched hand covers
The distance between two stars, about how far apart in arc degrees are the stars? (ii)The apparent
Size of Moon X as observed from Planet X is about 21 arc minutes. Approximately what part of an
Observer's thumb would cover Moon X?

Accepted Answer

A)  (i) 26 arc degrees; (ii) approximately $\frac { 1 } { 2 }$ of a thumb 
B)  (i) 60 arc degrees; (ii) approximately $\frac { 1 } { 3 }$ of a thumb 
C)  (i) 50 arc degrees; (ii) approximately $\frac { 1 } { 4 }$ of a thumb 
D)  (i) 61 arc degrees; (ii) approximately $\frac { 1 } { 5 }$ of a thumb 
A)  (i) 26 arc degrees; (ii) approximately $\frac { 1 } { 2 }$ of a thumb 
B)  (i) 60 arc degrees; (ii) approximately $\frac { 1 } { 3 }$ of a thumb 
C)  (i) 50 arc degrees; (ii) approximately $\frac { 1 } { 4 }$ of a thumb 
D)  (i) 61 arc degrees; (ii) approximately $\frac { 1 } { 5 }$ of a thumb B

Question 3

Identify the quadrant for the angle satisfying the following conditions.
-sin ϴ > 0 and cos ϴ > 0

Accepted Answer

A) Quadrant II 
B) Quadrant IV 
C) Quadrant I 
D) Quadrant III 
A) Quadrant II 
B) Quadrant IV 
C) Quadrant I 
D) Quadrant III C

Question 4

Use the properties of angle measures to find the measure of each marked angle.
-65°

Accepted Answer

A)  $245^{\circ} \text { and }-115^{\circ}$
  
B)  $425^{\circ} \text { and }-295^{\circ}$
  
C)  $245 ^ { \circ }$ and $- 115 ^ { \circ }$
  
D) $425^{\circ} \text { and }-295^{\circ}$
  
A)  $245^{\circ} \text { and }-115^{\circ}$
  
B)  $425^{\circ} \text { and }-295^{\circ}$
  
C)  $245 ^ { \circ }$ and $- 115 ^ { \circ }$
  
D) $425^{\circ} \text { and }-295^{\circ}$

Question 5

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene.
-76°22´ - 31°48´

Accepted Answer

A) 45°48´ 
B) 45°26´ 
C) 44°34´ 
D) 107°70´ 
A) 45°48´ 
B) 45°26´ 
C) 44°34´ 
D) 107°70´

Question 6

18
Suppose that is in standard position and the given point is on the terminal side of . Give the exact value of the
indicated trig function for .
-Find $\tan \theta$, given that $\sin \theta = \frac { 3 } { 4 }$ and $\theta$ is in quadrant II.

Accepted Answer

A)  $\frac { 5 } { 4 }$ 
B)  $- \frac { 3 \sqrt { 7 } } { 7 }$ 
C)  $- \frac { 3 } { 2 }$ 
D)  $- \frac { \sqrt { 7 } } { 9 }$ 
A)  $\frac { 5 } { 4 }$ 
B)  $- \frac { 3 \sqrt { 7 } } { 7 }$ 
C)  $- \frac { 3 } { 2 }$ 
D)  $- \frac { \sqrt { 7 } } { 9 }$

Question 7

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene.
-

Accepted Answer

A)  Acute, equilateral 
B)  Obtuse, isosceles 
C)  Obtuse, equilateral 
D)  Acute, scalene 
A)  Acute, equilateral 
B)  Obtuse, isosceles 
C)  Obtuse, equilateral 
D)  Acute, scalene

Question 8

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal
side of .
-(-2, 5)

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 9

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene.
-

Accepted Answer

A)  Obtuse, equilateral 
B)  Acute, isosceles 
C)  Obtuse, scalene 
D)  Acute, scalene 
A)  Obtuse, equilateral 
B)  Acute, isosceles 
C)  Obtuse, scalene 
D)  Acute, scalene

Question 10

Provide an appropriate response.
-Find the supplement of an angle whose measure is 74°31´.

Accepted Answer

A) 105°29´ 
B) 106°29´ 
C) 15°29´ 
D) 105°31´ 
A) 105°29´ 
B) 106°29´ 
C) 15°29´ 
D) 105°31´

Question 11

Use the fundamental identities to find the value of the trigonometric function.
-A triangle drawn on a map has sides of lengths 7 cm, 11 cm, and 15 cm. The shortest of the corresponding real-life distances is 92 km. Find the longest of the real-life distances.

Accepted Answer

A) 207.1 km 
B) 144.6 km 
C) 134.6 km 
D) 197.1 km 
A) 207.1 km 
B) 144.6 km 
C) 134.6 km 
D) 197.1 km

Question 12

Find the measure of the third angle of a triangle if the measures of the other two angles are given.
-cos (500°)and tan (500°)

Accepted Answer

A) negative and negative 
B) negative and positive 
C) positive and positive 
D) positive and negative 
A) negative and negative 
B) negative and positive 
C) positive and positive 
D) positive and negative

Question 13

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle.
-$\sin \theta > 0$ and $\cos \theta < 0$

Accepted Answer

A)  Quadrant IV 
B)  Quadrant II 
C)  Quadrant III 
D)  Quadrant I 
A)  Quadrant IV 
B)  Quadrant II 
C)  Quadrant III 
D)  Quadrant I

Question 14

Identify the quadrant for the angle satisfying the following conditions.
-A surveyor recording data for a new subdivision measured an angle as 11.77°. The next day, a different surveyor measured the same angle as 11°31´. Find the difference between these
Measurements (i)to the nearest minute and (ii)to the nearest hundredth of a degree.

Accepted Answer

A) (i)15´ (ii)0.25° 
B) (i)38´ (ii)0.43° 
C) (i)77´ (ii)1.29° 
D) (i)46´ (ii)0.46° 
A) (i)15´ (ii)0.25° 
B) (i)38´ (ii)0.43° 
C) (i)77´ (ii)1.29° 
D) (i)46´ (ii)0.46°

Question 15

Place your graphing calculator in parametric and degree modes. Set the window for Tmin=0, Tmax=360, Tstep=1, Xmin= $- 1.8 , X _ { \max } = 1.8 , X _ { \text {scl } } = 1 , \mathrm { Y } _ { \min } = - 1.2 , \mathrm { Y } _ { \max } = 1.2 , \mathrm { Y } s \mathrm {~s} = 1$. Set the functions to $\mathrm { X } _ { 1 \mathrm {~T} } = \cos \mathrm { T } ^ { \mathrm { Y } } , \mathrm { Y } _ { 1 \mathrm {~T} } = \sin \mathrm { T }$. Graph the circle of radius 1 on the screen. Use the trace feature to move a short distance around the circle.
--116°

Accepted Answer

A) ° 
B) 116° 
C) 244° 
D) 424 
A) ° 
B) 116° 
C) 244° 
D) 424

Question 16

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal
side of .
-358°45´12´´

Accepted Answer

A) 358.75° 
B) 358.71° 
C) 358.76° 
D) 358.81° 
A) 358.75° 
B) 358.71° 
C) 358.76° 
D) 358.81°

Question 17

Perform the calculation.
-$$90 ^ { \circ } - 34 ^ { \circ } 28 ^ { \prime } 50 ^ { \prime \prime }$$

Accepted Answer

A)  $55 ^ { \circ } 31 ^ { \prime } 10 ^ { \prime \prime }$ 
B)  $56 ^ { \circ } 32 ^ { \prime } 10 ^ { \prime \prime }$ 
C)  $55 ^ { \circ } 31 ^ { \prime } 9 ^ { \prime \prime }$ 
D)  $55 ^ { \circ } 32 ^ { \prime } 10 ^ { \prime \prime }$ 
A)  $55 ^ { \circ } 31 ^ { \prime } 10 ^ { \prime \prime }$ 
B)  $56 ^ { \circ } 32 ^ { \prime } 10 ^ { \prime \prime }$ 
C)  $55 ^ { \circ } 31 ^ { \prime } 9 ^ { \prime \prime }$ 
D)  $55 ^ { \circ } 32 ^ { \prime } 10 ^ { \prime \prime }$

Question 18

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.
-8 tan 0° + 3 csc 270°

Accepted Answer

A) 3 
B) Undefined 
C) -3 
D) 0 
A) 3 
B) Undefined 
C) -3 
D) 0

Question 19

Solve the problem. Round answers to the nearest tenth if necessary.
-Find the supplement of an angle whose measure is 60°.

Accepted Answer

A) 150° 
B) 240° 
C) 120° 
D) 30° 
A) 150° 
B) 240° 
C) 120° 
D) 30°

Question 20

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure
of two other angles, one positive and one negative, coterminal with the given angle.
-295°

Accepted Answer

A)  $65 ^ { \circ }$ and $- 65 ^ { \circ }$
  
B)  $755 ^ { \circ }$ and $- 105 ^ { \circ }$
  
C)  $85 ^ { \circ }$ and $- 95 ^ { \circ }$
  
D)  $655 ^ { \circ }$ and $- 65 ^ { \circ }$
  
A)  $65 ^ { \circ }$ and $- 65 ^ { \circ }$
  
B)  $755 ^ { \circ }$ and $- 105 ^ { \circ }$
  
C)  $85 ^ { \circ }$ and $- 95 ^ { \circ }$
  
D)  $655 ^ { \circ }$ and $- 65 ^ { \circ }$

Use the properties of angle measures to find the measure of each marked angle. -tan ϴ > 0 and sin ϴ < 0

Identify the quadrant for the angle satisfying the following conditions. -sin ϴ > 0 and cos ϴ > 0

Use the properties of angle measures to find the measure of each marked angle. -65°

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene. -76°22´ - 31°48´

18 Suppose that is in standard position and the given point is on the terminal side of . Give the exact value of the indicated trig function for . -Find $\tan \theta$ , given that $\sin \theta = \frac { 3 } { 4 }$ and $\theta$ is in quadrant II.

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene. -

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of . -(-2, 5)

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene. -

Provide an appropriate response. -Find the supplement of an angle whose measure is 74°31´.

Use the fundamental identities to find the value of the trigonometric function. -A triangle drawn on a map has sides of lengths 7 cm, 11 cm, and 15 cm. The shortest of the corresponding real-life distances is 92 km. Find the longest of the real-life distances.

Find the measure of the third angle of a triangle if the measures of the other two angles are given. -cos (500°)and tan (500°)

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. - $\sin \theta > 0$ and $\cos \theta < 0$

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of . -358°45´12´´

Perform the calculation. - $90 ^ { \circ } - 34 ^ { \circ } 28 ^ { \prime } 50 ^ { \prime \prime }$

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. -8 tan 0° + 3 csc 270°

Solve the problem. Round answers to the nearest tenth if necessary. -Find the supplement of an angle whose measure is 60°.

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. -295°

Acute Angles and Right Triangles

Radian Measure and the Unit Circle

Graphs of the Circular Functions

Trigonometric Identities

Inverse Circular Functions and Trigonometric Equations

Applications of Trigonometry and Vectors

Complex Numbers, Polar Equations, and Parametric Equations

Filters

Exam 1: Trigonometric Functions

Use the properties of angle measures to find the measure of each marked angle. -tan ϴ > 0 and sin ϴ < 0

Identify the quadrant for the angle satisfying the following conditions. -sin ϴ > 0 and cos ϴ > 0

Use the properties of angle measures to find the measure of each marked angle. -65°

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene. -76°22´ - 31°48´

18 Suppose that is in standard position and the given point is on the terminal side of . Give the exact value of the indicated trig function for . -Find tan⁡θ\tan \thetatanθ , given that sin⁡θ=34\sin \theta = \frac { 3 } { 4 }sinθ=43​ and θ\thetaθ is in quadrant II.

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene. -

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of . -(-2, 5)

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene. -

Provide an appropriate response. -Find the supplement of an angle whose measure is 74°31´.

Use the fundamental identities to find the value of the trigonometric function. -A triangle drawn on a map has sides of lengths 7 cm, 11 cm, and 15 cm. The shortest of the corresponding real-life distances is 92 km. Find the longest of the real-life distances.

Find the measure of the third angle of a triangle if the measures of the other two angles are given. -cos (500°)and tan (500°)

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. - sin⁡θ>0\sin \theta > 0sinθ>0 and cos⁡θ<0\cos \theta < 0cosθ<0

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of . -358°45´12´´

Perform the calculation. - 90∘−34∘28′50′′90 ^ { \circ } - 34 ^ { \circ } 28 ^ { \prime } 50 ^ { \prime \prime }90∘−34∘28′50′′

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. -8 tan 0° + 3 csc 270°

Solve the problem. Round answers to the nearest tenth if necessary. -Find the supplement of an angle whose measure is 60°.

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. -295°

Acute Angles and Right Triangles

Radian Measure and the Unit Circle

Graphs of the Circular Functions

Trigonometric Identities

Inverse Circular Functions and Trigonometric Equations

Applications of Trigonometry and Vectors

Complex Numbers, Polar Equations, and Parametric Equations

Filters

18 Suppose that is in standard position and the given point is on the terminal side of . Give the exact value of the indicated trig function for . -Find $\tan \theta$ , given that $\sin \theta = \frac { 3 } { 4 }$ and $\theta$ is in quadrant II.

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. - $\sin \theta > 0$ and $\cos \theta < 0$

Perform the calculation. - $90 ^ { \circ } - 34 ^ { \circ } 28 ^ { \prime } 50 ^ { \prime \prime }$