Question 1

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 .
-(18, 24); Find csc ϴ.

Accepted Answer

A)  $\frac { 4 } { 3 }$ 
B)  $\frac { 3 } { 4 }$ 
C)  $\frac { 5 } { 3 }$ 
D)  $\frac { 5 } { 4 }$ 
A)  $\frac { 4 } { 3 }$ 
B)  $\frac { 3 } { 4 }$ 
C)  $\frac { 5 } { 3 }$ 
D)  $\frac { 5 } { 4 }$

Question 2

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

$a = ( 4 x + 14 ) ^ { \circ } , b = ( 5 x + 31 ) ^ { \circ }$

Accepted Answer

A)  $5 ^ { \circ } , 175 ^ { \circ }$ 
B)  $34 ^ { \circ } , 56 ^ { \circ }$ 
C)  $5 ^ { \circ } , 85 ^ { \circ }$ 
D)  $34 ^ { \circ } , 31 ^ { \circ }$ 
A)  $5 ^ { \circ } , 175 ^ { \circ }$ 
B)  $34 ^ { \circ } , 56 ^ { \circ }$ 
C)  $5 ^ { \circ } , 85 ^ { \circ }$ 
D)  $34 ^ { \circ } , 31 ^ { \circ }$

Question 3

Use the fundamental identities to find the value of the trigonometric function.
-$\cos \theta < 0$ and $\csc \theta < 0$

Accepted Answer

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

Question 4

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.
-tan(n · 180°)

Accepted Answer

A) 0 
B) 1 
C) Undefined 
D) -1 
A) 0 
B) 1 
C) Undefined 
D) -1

Question 5

Use the fundamental identities to find the value of the trigonometric function.
-Find $\tan \theta$, given that $\sec \theta = \frac { 3 } { 2 }$ and $\theta$ is in quadrant IV.

Accepted Answer

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

Question 6

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

Accepted Answer

A)  $50 ^ { \circ }$ and $40 ^ { \circ }$ 
B)  $100 ^ { \circ }$ and $80 ^ { \circ }$ 
C)  $200 ^ { \circ }$ and $160 ^ { \circ }$ 
D)  $95 ^ { \circ }$ and $85 ^ { \circ }$ 
A)  $50 ^ { \circ }$ and $40 ^ { \circ }$ 
B)  $100 ^ { \circ }$ and $80 ^ { \circ }$ 
C)  $200 ^ { \circ }$ and $160 ^ { \circ }$ 
D)  $95 ^ { \circ }$ and $85 ^ { \circ }$

Question 7

Identify the quadrant for the angle satisfying the following conditions.
-22.66°

Accepted Answer

A) 22°39´66´´ 
B) 22°39´42´´ 
C) 22°39´24´´ 
D) 22°39´36´´ 
A) 22°39´66´´ 
B) 22°39´42´´ 
C) 22°39´24´´ 
D) 22°39´36´´

Question 8

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle.
-For what angle $\mathrm { T }$ is $\cos \mathrm { T } \approx 0.766$ ? (Assume $0 ^ { \circ } \leq \mathrm { T } \leq 90 ^ { \circ }$.)

Accepted Answer

A)  $36.832 ^ { \circ }$ 
B)  $50 ^ { \circ }$ 
C)  $40 ^ { \circ }$ 
D)  $0.766 ^ { \circ }$ 
A)  $36.832 ^ { \circ }$ 
B)  $50 ^ { \circ }$ 
C)  $40 ^ { \circ }$ 
D)  $0.766 ^ { \circ }$

Question 9

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle.
-$( 0 , - 9 )$; Find $\cos \theta$.

Accepted Answer

A)  $- 9$ 
B)  9 
C)  1 
D)  0 
A)  $- 9$ 
B)  9 
C)  1 
D)  0

Question 10

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 .
-$( - 5,12 )$; Find $\sin \theta$.

Accepted Answer

A)  $- \frac { 5 } { 13 }$ 
B)  $\frac { 5 } { 13 }$ 
C)  $\frac { 12 } { 13 }$ 
D)  $- \frac { 12 } { 13 }$ 
A)  $- \frac { 5 } { 13 }$ 
B)  $\frac { 5 } { 13 }$ 
C)  $\frac { 12 } { 13 }$ 
D)  $- \frac { 12 } { 13 }$

Question 11

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal
side of .
-20°

Accepted Answer

A)  $380 ^ { \circ }$ and $- 340 ^ { \circ }$
  
B)  $200 ^ { \circ }$ and $- 160 ^ { \circ }$
  
C) $200^{\circ} \text { and }-160^{\circ}$
  
D) $380^{\circ} \text { and }-340^{\circ}$
  
A)  $380 ^ { \circ }$ and $- 340 ^ { \circ }$
  
B)  $200 ^ { \circ }$ and $- 160 ^ { \circ }$
  
C) $200^{\circ} \text { and }-160^{\circ}$
  
D) $380^{\circ} \text { and }-340^{\circ}$

Question 12

Use the fundamental identities to find the value of the trigonometric function.
-Find $\sin \theta$, given that $\cos \theta = \frac { 2 } { 3 }$ and $\theta$ is in quadrant IV.

Accepted Answer

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

Question 13

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal
side of .
-x  
$$\begin{array} { l } 
a = 25 \
b = 75 \
c = 52
\end{array}$$

Accepted Answer

A)  $x = 52$ 
B)  $x = 39$ 
C)  $x = 26$ 
D)  $x = 13$ 
A)  $x = 52$ 
B)  $x = 39$ 
C)  $x = 26$ 
D)  $x = 13$

Question 14

Find the measure of each angle in the problem.
- 
$a=(2 x+8)^{\circ}$
$b = ( 4 x - 62 ) ^ { \circ }$

Accepted Answer

A)  $55 ^ { \circ } , 55 ^ { \circ }$ 
B)  $- 16 ^ { \circ } , - 16 ^ { \circ }$ 
C)  $35 ^ { \circ } , 35 ^ { \circ }$ 
D)  $78 ^ { \circ } , 78 ^ { \circ }$ 
A)  $55 ^ { \circ } , 55 ^ { \circ }$ 
B)  $- 16 ^ { \circ } , - 16 ^ { \circ }$ 
C)  $35 ^ { \circ } , 35 ^ { \circ }$ 
D)  $78 ^ { \circ } , 78 ^ { \circ }$

Question 15

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal
side of .
-(3, -6)

Accepted Answer

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

Question 16

Find the measure of the third angle of a triangle if the measures of the other two angles are given.
-35.5° and 86.1°

Accepted Answer

A) 148.4° 
B) 28.4° 
C) 58.4° 
D) 238.4° 
A) 148.4° 
B) 28.4° 
C) 58.4° 
D) 238.4°

Question 17

Evaluate the expression.
-$\tan \theta < 0$ and $\sin \theta < 0$

Accepted Answer

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

Question 18

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.
-Find $\csc \theta$, given that $\cot \theta = - \frac { 7 } { 2 }$ and $\cos \theta < 0$.

Accepted Answer

A)  $- \frac { \sqrt { 53 } } { 7 }$ 
B)  $\frac { 7 \sqrt { 53 } } { 53 }$ 
C)  $- \frac { 7 \sqrt { 53 } } { 53 }$ 
D)  $\frac { \sqrt { 53 } } { 2 }$ 
A)  $- \frac { \sqrt { 53 } } { 7 }$ 
B)  $\frac { 7 \sqrt { 53 } } { 53 }$ 
C)  $- \frac { 7 \sqrt { 53 } } { 53 }$ 
D)  $\frac { \sqrt { 53 } } { 2 }$

Question 19

Solve the problem. Round answers to the nearest tenth if necessary.
-A tree casts a shadow 38 m long. At the same time, the shadow cast by a 37-centimeter-tall statue is 75 cm long. Find the height of the tree.

Accepted Answer

A) 75.5 m 
B) 18.7 m 
C) 17.2 m 
D) 77.0 m 
A) 75.5 m 
B) 18.7 m 
C) 17.2 m 
D) 77.0 m

Question 20

Provide an appropriate response.
-For what angle $\mathrm { T }$ is $\cos \mathrm { T } \approx 0.866$ ? (Assume $0 ^ { \circ } \leq \mathrm { T } \leq 90 ^ { \circ }$.)

Accepted Answer

A)  $0.866 ^ { \circ }$ 
B)  $28.65 ^ { \circ }$ 
C)  $30 ^ { \circ }$ 
D)  $60 ^ { \circ }$ 
A)  $0.866 ^ { \circ }$ 
B)  $28.65 ^ { \circ }$ 
C)  $30 ^ { \circ }$ 
D)  $60 ^ { \circ }$

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 . -(18, 24); Find csc ϴ.

Use the fundamental identities to find the value of the trigonometric function. - $\cos \theta < 0$ and $\csc \theta < 0$

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. -tan(n · 180°)

Use the fundamental identities to find the value of the trigonometric function. -Find $\tan \theta$ , given that $\sec \theta = \frac { 3 } { 2 }$ and $\theta$ is in quadrant IV.

Identify the quadrant for the angle satisfying the following conditions. -22.66°

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. -For what angle $\mathrm { T }$ is $\cos \mathrm { T } \approx 0.766$ ? (Assume $0 ^ { \circ } \leq \mathrm { T } \leq 90 ^ { \circ }$ .)

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. - $( 0 , - 9 )$ ; Find $\cos \theta$ .

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 . - $( - 5,12 )$ ; Find $\sin \theta$ .

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of . -20°

Use the fundamental identities to find the value of the trigonometric function. -Find $\sin \theta$ , given that $\cos \theta = \frac { 2 } { 3 }$ and $\theta$ is in quadrant IV.

Find the measure of each angle in the problem. - $Find the measure of each angle in the problem. - a=(2 x+8)^{\circ} b = ( 4 x - 62 ) ^ { \circ }$ $a=(2 x+8)^{\circ}$ $b = ( 4 x - 62 ) ^ { \circ }$

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of . -(3, -6)

Find the measure of the third angle of a triangle if the measures of the other two angles are given. -35.5° and 86.1°

Evaluate the expression. - $\tan \theta < 0$ and $\sin \theta < 0$

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. -Find $\csc \theta$ , given that $\cot \theta = - \frac { 7 } { 2 }$ and $\cos \theta < 0$ .

Solve the problem. Round answers to the nearest tenth if necessary. -A tree casts a shadow 38 m long. At the same time, the shadow cast by a 37-centimeter-tall statue is 75 cm long. Find the height of the tree.

Provide an appropriate response. -For what angle $\mathrm { T }$ is $\cos \mathrm { T } \approx 0.866$ ? (Assume $0 ^ { \circ } \leq \mathrm { T } \leq 90 ^ { \circ }$ .)

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

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 . -(18, 24); Find csc ϴ.

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene. - a=(4x+14)∘,b=(5x+31)∘a = ( 4 x + 14 ) ^ { \circ } , b = ( 5 x + 31 ) ^ { \circ }a=(4x+14)∘,b=(5x+31)∘

Use the fundamental identities to find the value of the trigonometric function. - cos⁡θ<0\cos \theta < 0cosθ<0 and csc⁡θ<0\csc \theta < 0cscθ<0