Question 1

Find a value of ϴsuch that 0 ϴ 90° and ϴsatisfies the statement.
-cos ϴ= 0.2334

Accepted Answer

A) 13.50° 
B) 13.14° 
C) 76.50° 
D) -13.50° 
A) 13.50° 
B) 13.14° 
C) 76.50° 
D) -13.50°

Question 2

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative.
-II, $\frac { y } { x }$

Accepted Answer

A)  Positive 
B)  Negative 
A)  Positive 
B)  Negative

Question 3

Find the signs of the six trigonometric functions for the given angle.
-103°

Accepted Answer

A) Negative: all 
B) Positive: tangent and cotangent; negative: sine, cosine, secant, cosecant 
C) Positive: cosine and secant; negative: sine, tangent, cotangent, cosecant 
D) Positive: sine and cosecant; negative: cosine, tangent, cotangent, secant 
A) Negative: all 
B) Positive: tangent and cotangent; negative: sine, cosine, secant, cosecant 
C) Positive: cosine and secant; negative: sine, tangent, cotangent, cosecant 
D) Positive: sine and cosecant; negative: cosine, tangent, cotangent, secant

Question 4

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$. Give the exact value of the indicated trig function for $\theta$. Rationalize the denominator if necessary. If the function is undefined, say so.
-$( - 5,2 )$; find $\tan \theta$.

Accepted Answer

A)  $- \frac { 5 } { 2 }$ 
B)  $- \frac { 2 } { 5 }$ 
C)  $\frac { 2 } { 5 }$ 
D)  - 1 
A)  $- \frac { 5 } { 2 }$ 
B)  $- \frac { 2 } { 5 }$ 
C)  $\frac { 2 } { 5 }$ 
D)  - 1

Question 5

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$. Give the exact value of the indicated trig function for $\theta$. Rationalize the denominator if necessary. If the function is undefined, say so.
-$( - 4,7 )$; find $\cos \theta$

Accepted Answer

A)  $- \frac { 7 } { 4 }$ 
B)  $- \frac { 4 } { 7 }$ 
C)  $\frac { 7 \sqrt { 65 } } { 65 }$ 
D)  $- \frac { 4 \sqrt { 65 } } { 65 }$ 
A)  $- \frac { 7 } { 4 }$ 
B)  $- \frac { 4 } { 7 }$ 
C)  $\frac { 7 \sqrt { 65 } } { 65 }$ 
D)  $- \frac { 4 \sqrt { 65 } } { 65 }$

Question 6

Supplement of 4.2°

Accepted Answer

A) 85.8° 
B) 355.8° 
C) 130.8° 
D) 175.8° 
A) 85.8° 
B) 355.8° 
C) 130.8° 
D) 175.8°

Question 7

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-177°44'9''

Accepted Answer

A) 177.80 
B) 177.75 
C) 177.70 
D) 177.74 
A) 177.80 
B) 177.75 
C) 177.70 
D) 177.74

Question 8

Find the angle of smallest possible positive measure coterminal with the given angle.
--212°

Accepted Answer

A) -32° 
B) 148° 
C) 212° 
D) 328° 
A) -32° 
B) 148° 
C) 212° 
D) 328°

Question 9

Use a calculator to find the function value to four decimal places.
-cos (-418°)

Accepted Answer

A) 0.5299 
B) 0.8829 
C) -0.8480 
D) 0.0349 
A) 0.5299 
B) 0.8829 
C) -0.8480 
D) 0.0349

Question 10

Find the reference angle for the given angle.
-A = 143°

Accepted Answer

A) 53° 
B) 63° 
C) 47° 
D) 37° 
A) 53° 
B) 63° 
C) 47° 
D) 37°

Question 11

$\sec \left( - 60 ^ { \circ } \right)$

Accepted Answer

A)  $- \frac { 2 \sqrt { 3 } } { 3 }$ 
B)  $- \frac { \sqrt { 2 } } { 2 }$ 
C)  2 
D)  $\frac { 1 } { 2 }$ 
A)  $- \frac { 2 \sqrt { 3 } } { 3 }$ 
B)  $- \frac { \sqrt { 2 } } { 2 }$ 
C)  2 
D)  $\frac { 1 } { 2 }$

Question 12

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$. Give the exact value of the indicated trig function for $\theta$. Rationalize the denominator if necessary. If the function is undefined, say so.
-(0, -1); find tan $\theta$

Accepted Answer

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

Question 13

Convert the angle to degrees, minutes, and seconds.
-246.63°

Accepted Answer

A) 246°37'48'' 
B) 246°38'47'' 
C) 246°47'63'' 
D) 246°37'63'' 
A) 246°37'48'' 
B) 246°38'47'' 
C) 246°47'63'' 
D) 246°37'63''

Question 14

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-135°18'28''

Accepted Answer

A) 135.32 
B) 135.31 
C) 135.37 
D) 135.27 
A) 135.32 
B) 135.31 
C) 135.37 
D) 135.27

Question 15

Convert the angle to degrees, minutes, and seconds.
-56.73°

Accepted Answer

A) 56°43'48'' 
B) 56°43'38'' 
C) 56°53'38'' 
D) 56°53'48'' 
A) 56°43'48'' 
B) 56°43'38'' 
C) 56°53'38'' 
D) 56°53'48''

Question 16

State in which quadrant the terminal side of the given angle lies.
--92.2°

Accepted Answer

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

Question 17

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative.
-II, $\frac { x } { y }$

Accepted Answer

A)  Positive 
B)  Negative 
A)  Positive 
B)  Negative

Question 18

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary.
-$\cos \theta$, if $\sec \theta = - 3$

Accepted Answer

A)  $- \frac { 1 } { 3 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $- \frac { 1 } { 2 }$ 
A)  $- \frac { 1 } { 3 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $- \frac { 1 } { 2 }$

Question 19

Find the exact function value if it exists.
-cos(-270°)

Accepted Answer

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

Question 20

Find a value of ϴsuch that 0 ϴ 90° and ϴsatisfies the statement.
-sin ϴ= 0.8214

Accepted Answer

A) 55.23° 
B) -55.23° 
C) 145.22° 
D) 39.40° 
A) 55.23° 
B) -55.23° 
C) 145.22° 
D) 39.40°

Find a value of ϴsuch that 0 ϴ 90° and ϴsatisfies the statement. -cos ϴ= 0.2334

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative. -II, $\frac { y } { x }$

Find the signs of the six trigonometric functions for the given angle. -103°

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$ . Give the exact value of the indicated trig function for $\theta$ . Rationalize the denominator if necessary. If the function is undefined, say so. - $( - 5,2 )$ ; find $\tan \theta$ .

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$ . Give the exact value of the indicated trig function for $\theta$ . Rationalize the denominator if necessary. If the function is undefined, say so. - $( - 4,7 )$ ; find $\cos \theta$

Supplement of 4.2°

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. -177°44'9''

Find the angle of smallest possible positive measure coterminal with the given angle. --212°

Use a calculator to find the function value to four decimal places. -cos (-418°)

Find the reference angle for the given angle. -A = 143°

$\sec \left( - 60 ^ { \circ } \right)$

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$ . Give the exact value of the indicated trig function for $\theta$ . Rationalize the denominator if necessary. If the function is undefined, say so. -(0, -1); find tan $\theta$

Convert the angle to degrees, minutes, and seconds. -246.63°

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. -135°18'28''

Convert the angle to degrees, minutes, and seconds. -56.73°

State in which quadrant the terminal side of the given angle lies. --92.2°

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative. -II, $\frac { x } { y }$

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary. - $\cos \theta$ , if $\sec \theta = - 3$

Find the exact function value if it exists. -cos(-270°)

Find a value of ϴsuch that 0 ϴ 90° and ϴsatisfies the statement. -sin ϴ= 0.8214

The Art of Problem Solving

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Exam 14: Trigonometry Formerly

Find a value of ϴsuch that 0 ϴ 90° and ϴsatisfies the statement. -cos ϴ= 0.2334

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative. -II, yx\frac { y } { x }xy​

Find the signs of the six trigonometric functions for the given angle. -103°

Supplement of 4.2°

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. -177°44'9''

Find the angle of smallest possible positive measure coterminal with the given angle. --212°

Use a calculator to find the function value to four decimal places. -cos (-418°)

Find the reference angle for the given angle. -A = 143°

sec⁡(−60∘)\sec \left( - 60 ^ { \circ } \right)sec(−60∘)

Suppose that θ\thetaθ is in standard position and the given point is on the terminal side of θ\thetaθ . Give the exact value of the indicated trig function for θ\thetaθ . Rationalize the denominator if necessary. If the function is undefined, say so. -(0, -1); find tan θ\thetaθ

Convert the angle to degrees, minutes, and seconds. -246.63°

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. -135°18'28''

Convert the angle to degrees, minutes, and seconds. -56.73°

State in which quadrant the terminal side of the given angle lies. --92.2°

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative. -II, xy\frac { x } { y }yx​

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary. - cos⁡θ\cos \thetacosθ , if sec⁡θ=−3\sec \theta = - 3secθ=−3

Find the exact function value if it exists. -cos(-270°)

Find a value of ϴsuch that 0 ϴ 90° and ϴsatisfies the statement. -sin ϴ= 0.8214

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Graph Theory

Voting and Apportionment

Filters

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative. -II, $\frac { y } { x }$

$\sec \left( - 60 ^ { \circ } \right)$

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$ . Give the exact value of the indicated trig function for $\theta$ . Rationalize the denominator if necessary. If the function is undefined, say so. -(0, -1); find tan $\theta$

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative. -II, $\frac { x } { y }$

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary. - $\cos \theta$ , if $\sec \theta = - 3$