Question 1

Evaluate the expression.
-Find $\cot \theta$, given that $\cos \theta = \frac { 15 } { 17 }$ and $\theta$ is in quadrant IV.

Accepted Answer

A)  $\frac { 17 } { 15 }$ 
B)  $- \frac { 15 \sqrt { 2 } } { 2 }$ 
C)  $- \frac { 15 } { 8 }$ 
D)  $- \frac { 8 } { 15 }$ 
A)  $\frac { 17 } { 15 }$ 
B)  $- \frac { 15 \sqrt { 2 } } { 2 }$ 
C)  $- \frac { 15 } { 8 }$ 
D)  $- \frac { 8 } { 15 }$

Question 2

An equation of the terminal side of an angle in standard position is given along with a restriction on x. Find the
indicated trigonometric function value of . Do not use a calculator.
-$\angle \mathrm { C }$.

$\mathrm { m } \angle \mathrm { E } = 27 ^ { \circ }$

Accepted Answer

A)  $107 ^ { \circ }$ 
B)  $56 ^ { \circ }$ 
C)  $27 ^ { \circ }$ 
D)  $97 ^ { \circ }$ 
A)  $107 ^ { \circ }$ 
B)  $56 ^ { \circ }$ 
C)  $27 ^ { \circ }$ 
D)  $97 ^ { \circ }$

Question 3

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

Accepted Answer

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

Question 4

The triangles are similar. Find the missing side, angle or value of the variable.
-

$a = 13$
$b = 12$
$c = 5$
$d = 26$
$e = 24$

Accepted Answer

A)  $x = 15$ 
B)  $x = 5$ 
C)  $x = 7$ 
D)  $x = 10$ 
A)  $x = 15$ 
B)  $x = 5$ 
C)  $x = 7$ 
D)  $x = 10$

Question 5

Perform the calculation.
-$\cot \theta  0$

Accepted Answer

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

Question 6

Provide an appropriate response.
-Find the supplement of an angle whose measure is $37 ^ { \circ } 39 ^ { \prime } 17 ^ { \prime \prime }$

Accepted Answer

A)  $52 ^ { \circ } 21 ^ { \prime } 43 ^ { \prime \prime }$ 
B)  $142 ^ { \circ } 20 ^ { \prime } 43 ^ { \prime \prime }$ 
C)  $142 ^ { \circ } 21 ^ { \prime } 43 ^ { \prime \prime }$ 
D)  $52 ^ { \circ } 20 ^ { \prime } 43 ^ { \prime \prime }$ 
A)  $52 ^ { \circ } 21 ^ { \prime } 43 ^ { \prime \prime }$ 
B)  $142 ^ { \circ } 20 ^ { \prime } 43 ^ { \prime \prime }$ 
C)  $142 ^ { \circ } 21 ^ { \prime } 43 ^ { \prime \prime }$ 
D)  $52 ^ { \circ } 20 ^ { \prime } 43 ^ { \prime \prime }$

Question 7

Use the fundamental identities to find the value of the trigonometric function.
-

Accepted Answer

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

Question 8

Decide whether the statement is possible or impossible for an angle .
-$\cos \theta = \frac { 2 } { 11 }$ and $\sec \theta = \frac { 11 } { 2 }$

Accepted Answer

A)  Possible 
B)  Impossible 
A)  Possible 
B)  Impossible

Question 9

Decide whether the statement is possible or impossible for an angle .
-BA

Accepted Answer

A)  $\mathrm { RT }$ 
B)  Cannot be determined 
C)  $\mathrm { ST }$ 
D)  $\mathrm { RS }$ 
A)  $\mathrm { RT }$ 
B)  Cannot be determined 
C)  $\mathrm { ST }$ 
D)  $\mathrm { RS }$

Question 10

$$\text { Decide whether the statement is possible or impossible for an angle } \theta \text {. }$$
-Two quadrilaterals (four-sided figures)are similar. The lengths of the three longest sides of the first quadrilateral are 24 ft, 16 ft, and 12 ft. The lengths of the two shortest sides of the second
Quadrilateral are 18 ft and 9 ft. Find the unknown lengths of the sides of these two figures.

Accepted Answer

A) The unknown side in the first quadrilateral is 10 ft. The two unknown sides in the second quadrilateral are 27 ft and 24 ft. 
B) The unknown side in the first quadrilateral is 8 ft. The two unknown sides in the second quadrilateral are 36 ft and 12 ft. 
C) Not enough information is provided. 
D) The unknown side in the first quadrilateral is 6 ft. The two unknown sides in the second quadrilateral are 36 ft and 24 ft. 
A) The unknown side in the first quadrilateral is 10 ft. The two unknown sides in the second quadrilateral are 27 ft and 24 ft. 
B) The unknown side in the first quadrilateral is 8 ft. The two unknown sides in the second quadrilateral are 36 ft and 12 ft. 
C) Not enough information is provided. 
D) The unknown side in the first quadrilateral is 6 ft. The two unknown sides in the second quadrilateral are 36 ft and 24 ft.

Question 11

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-211°44´29´´

Accepted Answer

A) 211.80° 
B) 211.70° 
C) 211.74° 
D) 211.75° 
A) 211.80° 
B) 211.70° 
C) 211.74° 
D) 211.75°

Question 12

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene.
-(12, 16); Find sin ϴ.

Accepted Answer

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

Question 13

Evaluate the expression.
-

Accepted Answer

A)  $60 ^ { \circ }$ and $40 ^ { \circ }$ 
B)  $108 ^ { \circ }$ and $72 ^ { \circ }$ 
C)  $100 ^ { \circ }$ and $80 ^ { \circ }$ 
D)  $216 ^ { \circ }$ and $144 ^ { \circ }$ 
A)  $60 ^ { \circ }$ and $40 ^ { \circ }$ 
B)  $108 ^ { \circ }$ and $72 ^ { \circ }$ 
C)  $100 ^ { \circ }$ and $80 ^ { \circ }$ 
D)  $216 ^ { \circ }$ and $144 ^ { \circ }$

Question 14

Identify the quadrant for the angle satisfying the following conditions.
-185°52´21´´

Accepted Answer

A) 185.93° 
B) 185.87° 
C) 185.83° 
D) 185.88° 
A) 185.93° 
B) 185.87° 
C) 185.83° 
D) 185.88°

Question 15

Use the fundamental identities to find the value of the trigonometric function.
-cos (-283°)and sin (-283°)

Accepted Answer

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

Question 16

Evaluate the expression.
- 
$a=(11 x+6)^{\circ}, b=(2 x+148)^{\circ}$

Accepted Answer

A)  $11 ^ { \circ } , 79 ^ { \circ }$ 
B)  $28 ^ { \circ } , 148 ^ { \circ }$ 
C)  $11 ^ { \circ } , 169 ^ { \circ }$ 
D)  $28 ^ { \circ } , 152 ^ { \circ }$ 
A)  $11 ^ { \circ } , 79 ^ { \circ }$ 
B)  $28 ^ { \circ } , 148 ^ { \circ }$ 
C)  $11 ^ { \circ } , 169 ^ { \circ }$ 
D)  $28 ^ { \circ } , 152 ^ { \circ }$

Question 17

Find the measure of the third angle of a triangle if the measures of the other two angles are given.
-27° and 101°

Accepted Answer

A) 128° 
B) 232° 
C) 38° 
D) 52° 
A) 128° 
B) 232° 
C) 38° 
D) 52°

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.
-28°23' and 95°22'

Accepted Answer

A) 236°55' 
B) 57°15' 
C) 56°15' 
D) 237°55' 
A) 236°55' 
B) 57°15' 
C) 56°15' 
D) 237°55'

Question 19

Use the fundamental identities to find the value of the trigonometric function.
-130°

Accepted Answer

A)  $\quad 490 ^ { \circ }$ and $- 230 ^ { \circ }$
  
B)  $310 ^ { \circ }$ and $- 50 ^ { \circ }$
  
C)  $490 ^ { \circ }$ and $- 230 ^ { \circ }$
  
D) $310 ^ { \circ }$ and $- 50 ^ { \circ }$
  
A)  $\quad 490 ^ { \circ }$ and $- 230 ^ { \circ }$
  
B)  $310 ^ { \circ }$ and $- 50 ^ { \circ }$
  
C)  $490 ^ { \circ }$ and $- 230 ^ { \circ }$
  
D) $310 ^ { \circ }$ and $- 50 ^ { \circ }$

Question 20

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.
-$\tan \theta$, given that $\cot \theta = \frac { \sqrt { 11 } } { 4 }$

Accepted Answer

A)  $\frac { 4 \sqrt { 11 } } { 11 }$ 
B)  $\frac { \sqrt { 11 } } { 11 }$ 
C)  $\frac { \sqrt { 4 } } { 11 }$ 
D)  $\frac { 11 \sqrt { 11 } } { 4 }$ 
A)  $\frac { 4 \sqrt { 11 } } { 11 }$ 
B)  $\frac { \sqrt { 11 } } { 11 }$ 
C)  $\frac { \sqrt { 4 } } { 11 }$ 
D)  $\frac { 11 \sqrt { 11 } } { 4 }$

Evaluate the expression. -Find $\cot \theta$ , given that $\cos \theta = \frac { 15 } { 17 }$ and $\theta$ is in quadrant IV.

The triangles are similar. Find the missing side, angle or value of the variable. - $a = 13$ $b = 12$ $c = 5$ $d = 26$ $e = 24$

Perform the calculation. - $\cot \theta < 0$ and $\cos \theta > 0$

Provide an appropriate response. -Find the supplement of an angle whose measure is $37 ^ { \circ } 39 ^ { \prime } 17 ^ { \prime \prime }$

Use the fundamental identities to find the value of the trigonometric function. -

Decide whether the statement is possible or impossible for an angle . - $\cos \theta = \frac { 2 } { 11 }$ and $\sec \theta = \frac { 11 } { 2 }$

Decide whether the statement is possible or impossible for an angle . -BA

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. -211°44´29´´

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene. -(12, 16); Find sin ϴ.

Evaluate the expression. -

Identify the quadrant for the angle satisfying the following conditions. -185°52´21´´

Use the fundamental identities to find the value of the trigonometric function. -cos (-283°)and sin (-283°)

Evaluate the expression. - $Evaluate the expression. - a=(11 x+6)^{\circ}, b=(2 x+148)^{\circ}$ $a=(11 x+6)^{\circ}, b=(2 x+148)^{\circ}$

Find the measure of the third angle of a triangle if the measures of the other two angles are given. -27° and 101°

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. -28°23' and 95°22'

Use the fundamental identities to find the value of the trigonometric function. -130°

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. - $\tan \theta$ , given that $\cot \theta = \frac { \sqrt { 11 } } { 4 }$

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

Evaluate the expression. -Find cot⁡θ\cot \thetacotθ , given that cos⁡θ=1517\cos \theta = \frac { 15 } { 17 }cosθ=1715​ and θ\thetaθ is in quadrant IV.

An equation of the terminal side of an angle in standard position is given along with a restriction on x. Find the indicated trigonometric function value of . Do not use a calculator. - ∠C\angle \mathrm { C }∠C . m∠E=27∘\mathrm { m } \angle \mathrm { E } = 27 ^ { \circ }m∠E=27∘

The triangles are similar. Find the missing side, angle or value of the variable. - a=13a = 13a=13 b=12b = 12b=12 c=5c = 5c=5 d=26d = 26d=26 e=24e = 24e=24

Perform the calculation. - cot⁡θ<0\cot \theta < 0cotθ<0 and cos⁡θ>0\cos \theta > 0cosθ>0

Provide an appropriate response. -Find the supplement of an angle whose measure is 37∘39′17′′37 ^ { \circ } 39 ^ { \prime } 17 ^ { \prime \prime }37∘39′17′′