Question 1

Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree.
-tan 4ϴ = 0

Accepted Answer

A) {0°, 45°, 90°, 135°, 180°, 225°, 270°} 
B) {0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°} 
C) {33°, 57°, 147°, 237°, 327°} 
D) {0°, 90°, 180°, 270°} 
A) {0°, 45°, 90°, 135°, 180°, 225°, 270°} 
B) {0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°} 
C) {33°, 57°, 147°, 237°, 327°} 
D) {0°, 90°, 180°, 270°}

Question 2

Solve the equation in the interval [0°, 360°). Give solutions to the nearest tenth, if necessary.
-$3 \sin ^ { 2 } \theta - \sin \theta - 4 = 0$

Accepted Answer

A)  $\left\{ 0 ^ { \circ } \right\}$ 
B)  $\left\{ 270 ^ { \circ } \right\}$ 
C)  $\left\{ 180 ^ { \circ } \right\}$ 
D)  $\left\{ 90 ^ { \circ } \right\}$ 
A)  $\left\{ 0 ^ { \circ } \right\}$ 
B)  $\left\{ 270 ^ { \circ } \right\}$ 
C)  $\left\{ 180 ^ { \circ } \right\}$ 
D)  $\left\{ 90 ^ { \circ } \right\}$

Question 3

Solve the equation for x, where x is restricted to the given interval.
-$$y = \cos ( x + 12 ) \text {, for } x \text { in } [ - 12 , \pi - 12 ]$$

Accepted Answer

A)  $x = \arccos y + 12$ 
B)  $x = \arccos ( y - 12 )$ 
C)  $x = \arccos ( y + 12 )$ 
D)  $x = \arccos y - 12$ 
A)  $x = \arccos y + 12$ 
B)  $x = \arccos ( y - 12 )$ 
C)  $x = \arccos ( y + 12 )$ 
D)  $x = \arccos y - 12$

Question 4

Solve the equation for x, where x is restricted to the given interval.
-$3 y = \tan 6 x$, for $x$ in $\left( - \frac { \pi } { 12 } , \frac { \pi } { 12 } \right)$

Accepted Answer

A)  $x = 6 \arctan \frac { y } { 3 }$ 
B)  $x = \frac { 1 } { 2 } \arctan y$ 
C)  $x = 2 \arctan y$ 
D)  $x = \frac { 1 } { 6 } \arctan 3 y$ 
A)  $x = 6 \arctan \frac { y } { 3 }$ 
B)  $x = \frac { 1 } { 2 } \arctan y$ 
C)  $x = 2 \arctan y$ 
D)  $x = \frac { 1 } { 6 } \arctan 3 y$

Question 5

Give the degree measure of .
-$\theta = \cot ^ { - 1 } ( \sqrt { 3 } )$

Accepted Answer

A)  $- 30 ^ { \circ }$ 
B)  $45 ^ { \circ }$ 
C)  $30 ^ { \circ }$ 
D)  $60 ^ { \circ }$ 
A)  $- 30 ^ { \circ }$ 
B)  $45 ^ { \circ }$ 
C)  $30 ^ { \circ }$ 
D)  $60 ^ { \circ }$

Question 6

Use a calculator to give the real number value. Round the answer to 7 decimal places.
-$$y = \cot ^ { - 1 } ( 2.5181552 )$$

Accepted Answer

A)  $2.1658824$ 
B)  $0.3780178$ 
C)  $6.8341176$ 
D)  $1.1927785$ 
A)  $2.1658824$ 
B)  $0.3780178$ 
C)  $6.8341176$ 
D)  $1.1927785$

Question 7

Solve the problem.
-Let $( a , b )$ and $( c , d )$ be two points in the first quadrant, and let $\theta$ be the angle between the line segment connecting $( a , b )$ with the origin and the line segment connecting $( c , d )$ with the origin. It can be shown that
$\cos \theta = \frac { a c + b d } { \sqrt { \left( a ^ { 2 } + b ^ { 2 } \right) \left( c ^ { 2 } + d ^ { 2 } \right) } }$
Find $\theta$ if $a = 7 , b = 5 , c = 2$, and $d = 8$. Give your answer in degrees rounded to the nearest hundredth.

Accepted Answer

A)  $111.50 ^ { \circ }$ 
B)  $40.43 ^ { \circ }$ 
C)  $55.68 ^ { \circ }$ 
D)  $78.62 ^ { \circ }$ 
A)  $111.50 ^ { \circ }$ 
B)  $40.43 ^ { \circ }$ 
C)  $55.68 ^ { \circ }$ 
D)  $78.62 ^ { \circ }$

Question 8

Write the following as an algebraic expression in u, u > 0.
-$\tan \left( \operatorname { arcsec } \frac { \sqrt { \mathrm { u } ^ { 2 } + 25 } } { \mathrm { u } } \right)$

Accepted Answer

A)  $5 \mathrm { u }$ 
B)  $\frac { u \sqrt { u ^ { 2 } + 25 } } { u ^ { 2 } + 25 }$ 
C)  $\frac { \sqrt { u ^ { 2 } + 5 } } { u ^ { 2 } + 5 }$ 
D)  $\frac { 5 } { u }$ 
A)  $5 \mathrm { u }$ 
B)  $\frac { u \sqrt { u ^ { 2 } + 25 } } { u ^ { 2 } + 25 }$ 
C)  $\frac { \sqrt { u ^ { 2 } + 5 } } { u ^ { 2 } + 5 }$ 
D)  $\frac { 5 } { u }$

Question 9

Solve the equation in the interval [0°, 360°). Give solutions to the nearest tenth, if necessary.
-$$\csc \theta = 1 + \cot \theta$$

Accepted Answer

A)  $\left\{ 90 ^ { \circ } \right\}$ 
B)  $\varnothing$ 
C)  $\left\{ 90 ^ { \circ } , 270 ^ { \circ } \right\}$ 
D)  $\left\{ 270 ^ { \circ } \right\}$ 
A)  $\left\{ 90 ^ { \circ } \right\}$ 
B)  $\varnothing$ 
C)  $\left\{ 90 ^ { \circ } , 270 ^ { \circ } \right\}$ 
D)  $\left\{ 270 ^ { \circ } \right\}$

Question 10

Solve the equation for x, where x is restricted to the given interval.
-$$y = 4 \cot \frac { x } { 2 } , \text { for } x \text { in } ( 0,2 \pi )$$

Accepted Answer

A)  $x = \frac { 1 } { 2 } \operatorname { arccot } 4 y$ 
B)  $x = \frac { 1 } { 2 } \operatorname { arccot } \frac { y } { 4 }$ 
C)  $x = 2 \operatorname { arccot } 4 y$ 
D)  $x = 2 \operatorname { arccot } \frac { y } { 4 }$ 
A)  $x = \frac { 1 } { 2 } \operatorname { arccot } 4 y$ 
B)  $x = \frac { 1 } { 2 } \operatorname { arccot } \frac { y } { 4 }$ 
C)  $x = 2 \operatorname { arccot } 4 y$ 
D)  $x = 2 \operatorname { arccot } \frac { y } { 4 }$

Question 11

Give the exact value of the expression.
-$\sin ( \arctan 2 )$

Accepted Answer

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

Question 12

Provide an appropriate response.
-$$\text { True or false? The statement } \cos \left( \cos ^ { - 1 } x \right) = x \text { for all real numbers in the interval } \infty \leq x \leq \infty \text {. }$$

Accepted Answer

A) True 
 B)False

Question 13

Solve.
-In the study of alternating electric current, capacitive voltage is given by $V _ { C } = - \frac { i } { 2 \pi f } \cos 2 \pi f \mathrm { ft }$, where $\mathrm { f }$ is the number of cycles per second, $\mathrm { i }$ is the maximum current, and $\mathrm { t }$ is the time in seconds. Solve the equation for $\mathrm { t }$.

Accepted Answer

A)  $\mathrm { t } = \frac { 1 } { 2 \pi \mathrm { f } } \arccos \left( \frac { 2 \pi \mathrm { fV } _ { \mathrm { C } } } { \mathrm { i } } \right)$ 
B)  $t = 2 \pi f \arccos \left( - \frac { 2 \pi f V _ { C } } { i } \right)$ 
C)  $\mathrm { t } = \frac { 1 } { 2 \pi \mathrm { f } } \arccos \left( - \frac { 2 \pi \mathrm { fV } _ { \mathrm { C } } } { \mathrm { i } } \right)$ 
D)  $t = 2 \pi f \cos \left( - \frac { 2 \pi \mathrm { fV } _ { \mathrm { C } } } { \mathrm { i } } \right)$ 
A)  $\mathrm { t } = \frac { 1 } { 2 \pi \mathrm { f } } \arccos \left( \frac { 2 \pi \mathrm { fV } _ { \mathrm { C } } } { \mathrm { i } } \right)$ 
B)  $t = 2 \pi f \arccos \left( - \frac { 2 \pi f V _ { C } } { i } \right)$ 
C)  $\mathrm { t } = \frac { 1 } { 2 \pi \mathrm { f } } \arccos \left( - \frac { 2 \pi \mathrm { fV } _ { \mathrm { C } } } { \mathrm { i } } \right)$ 
D)  $t = 2 \pi f \cos \left( - \frac { 2 \pi \mathrm { fV } _ { \mathrm { C } } } { \mathrm { i } } \right)$

Question 14

Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round to
one decimal place.
-On the given graph of $y = \cot x$ sketch the graph of $y = \cot ^ { - 1 } x$ as defined in the text. Give the domain and the range.

Accepted Answer

The answer of Use the parallelogram rule to find the...

Question 15

Solve the equation for exact solutions.
-$$\tan ^ { - 1 } ( x + 2 ) + \tan ^ { - 1 } x = \tan ^ { - 1 } \frac { 1 } { 4 }$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 2 } \right\}$ 
B)  $\{ 2 \rangle$ 
C)  $\{ - 5 + 3 \sqrt { 2 } \}$ 
D)  $\left\{ - \frac { 3 } { 4 } , \frac { 3 } { 4 } \right\}$ 
A)  $\left\{ \frac { 1 } { 2 } \right\}$ 
B)  $\{ 2 \rangle$ 
C)  $\{ - 5 + 3 \sqrt { 2 } \}$ 
D)  $\left\{ - \frac { 3 } { 4 } , \frac { 3 } { 4 } \right\}$

Question 16

Solve the equation for solutions over the interval $[ 0,2 \pi$ ). Write solutions as exact values or to four decimal places, as appropriate.
-$\tan 3 x - \sec 3 x = 5$

Accepted Answer

A)  $\{ 1.4392,3.5336,5.6280 \}$ 
B)  $\{ 1.9628,4.5808 \}$ 
C)  $\{ 5.8884,13.7424 \}$ 
D)  $\{ 4.3176,10.6008,16.8840 \}$ 
A)  $\{ 1.4392,3.5336,5.6280 \}$ 
B)  $\{ 1.9628,4.5808 \}$ 
C)  $\{ 5.8884,13.7424 \}$ 
D)  $\{ 4.3176,10.6008,16.8840 \}$

Question 17

Solve the equation in the interval [0°, 360°). Give solutions to the nearest tenth, if necessary.
-$4 \sin ^ { 2 } \theta = 3$

Accepted Answer

A)  $\varnothing$ 
B)  $\left\{ 60 ^ { \circ } , 120 ^ { \circ } \right\}$ 
C)  $\left\{ 60 ^ { \circ } , 120 ^ { \circ } , 240 ^ { \circ } , 300 ^ { \circ } \right\}$ 
D)  $\left\{ 240 ^ { \circ } , 300 ^ { \circ } \right\}$ 
A)  $\varnothing$ 
B)  $\left\{ 60 ^ { \circ } , 120 ^ { \circ } \right\}$ 
C)  $\left\{ 60 ^ { \circ } , 120 ^ { \circ } , 240 ^ { \circ } , 300 ^ { \circ } \right\}$ 
D)  $\left\{ 240 ^ { \circ } , 300 ^ { \circ } \right\}$

Question 18

Solve the equation for exact solutions.
-$$\cos ^ { - 1 } x = \sin ^ { - 1 } \frac { 5 } { 13 }$$

Accepted Answer

A)  $\{ 0 \}$ 
B)  $\left\{ \frac { 12 } { 5 } \right\}$ 
C)  $\left\{ \frac { 12 } { 13 } \right\}$ 
D)  $\varnothing$ 
A)  $\{ 0 \}$ 
B)  $\left\{ \frac { 12 } { 5 } \right\}$ 
C)  $\left\{ \frac { 12 } { 13 } \right\}$ 
D)  $\varnothing$

Question 19

Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree.
-$\tan ^ { 2 } 2 \theta = 5$

Accepted Answer

A)  $\left\{ 33 ^ { \circ } , 57 ^ { \circ } , 123 ^ { \circ } , 147 ^ { \circ } , 213 ^ { \circ } , 237 ^ { \circ } , 303 ^ { \circ } , 327 ^ { \circ } \right\}$ 
B)  $\left\{ 0 ^ { \circ } \right\}$ 
C)  $\left\{ 0 ^ { \circ } , 45 ^ { \circ } , 90 ^ { \circ } , 135 ^ { \circ } , 180 ^ { \circ } , 225 ^ { \circ } , 270 ^ { \circ } \right\}$ 
D)  $\left\{ 0 ^ { \circ } , 90 ^ { \circ } , 180 ^ { \circ } , 270 ^ { \circ } \right\}$ 
A)  $\left\{ 33 ^ { \circ } , 57 ^ { \circ } , 123 ^ { \circ } , 147 ^ { \circ } , 213 ^ { \circ } , 237 ^ { \circ } , 303 ^ { \circ } , 327 ^ { \circ } \right\}$ 
B)  $\left\{ 0 ^ { \circ } \right\}$ 
C)  $\left\{ 0 ^ { \circ } , 45 ^ { \circ } , 90 ^ { \circ } , 135 ^ { \circ } , 180 ^ { \circ } , 225 ^ { \circ } , 270 ^ { \circ } \right\}$ 
D)  $\left\{ 0 ^ { \circ } , 90 ^ { \circ } , 180 ^ { \circ } , 270 ^ { \circ } \right\}$

Question 20

Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree.
-$$\cos 2 \theta = \frac { \sqrt { 3 } } { 2 }$$

Accepted Answer

A)  $\left\{ 105 ^ { \circ } , 165 ^ { \circ } , 285 ^ { \circ } , 345 ^ { \circ } \right\}$ 
B)  $\left\{ 0 ^ { \circ } , 120 ^ { \circ } , 180 ^ { \circ } , 240 ^ { \circ } \right\}$ 
C)  $\left\{ 30 ^ { \circ } , 90 ^ { \circ } , 150 ^ { \circ } , 270 ^ { \circ } \right\}$ 
D)  $\left\{ 15 ^ { \circ } , 165 ^ { \circ } , 195 ^ { \circ } , 345 ^ { \circ } \right\}$ 
A)  $\left\{ 105 ^ { \circ } , 165 ^ { \circ } , 285 ^ { \circ } , 345 ^ { \circ } \right\}$ 
B)  $\left\{ 0 ^ { \circ } , 120 ^ { \circ } , 180 ^ { \circ } , 240 ^ { \circ } \right\}$ 
C)  $\left\{ 30 ^ { \circ } , 90 ^ { \circ } , 150 ^ { \circ } , 270 ^ { \circ } \right\}$ 
D)  $\left\{ 15 ^ { \circ } , 165 ^ { \circ } , 195 ^ { \circ } , 345 ^ { \circ } \right\}$

Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree. -tan 4ϴ = 0

Solve the equation in the interval [0°, 360°). Give solutions to the nearest tenth, if necessary. - $3 \sin ^ { 2 } \theta - \sin \theta - 4 = 0$

Solve the equation for x, where x is restricted to the given interval. - $y = \cos ( x + 12 ) \text {, for } x \text { in } [ - 12 , \pi - 12 ]$

Solve the equation for x, where x is restricted to the given interval. - $3 y = \tan 6 x$ , for $x$ in $\left( - \frac { \pi } { 12 } , \frac { \pi } { 12 } \right)$

Give the degree measure of . - $\theta = \cot ^ { - 1 } ( \sqrt { 3 } )$

Use a calculator to give the real number value. Round the answer to 7 decimal places. - $y = \cot ^ { - 1 } ( 2.5181552 )$

Write the following as an algebraic expression in u, u > 0. - $\tan \left( \operatorname { arcsec } \frac { \sqrt { \mathrm { u } ^ { 2 } + 25 } } { \mathrm { u } } \right)$

Solve the equation in the interval [0°, 360°). Give solutions to the nearest tenth, if necessary. - $\csc \theta = 1 + \cot \theta$

Solve the equation for x, where x is restricted to the given interval. - $y = 4 \cot \frac { x } { 2 } , \text { for } x \text { in } ( 0,2 \pi )$

Give the exact value of the expression. - $\sin ( \arctan 2 )$

Provide an appropriate response. - $\text { True or false? The statement } \cos \left( \cos ^ { - 1 } x \right) = x \text { for all real numbers in the interval } \infty \leq x \leq \infty \text {. }$

Solve the equation for exact solutions. - $\tan ^ { - 1 } ( x + 2 ) + \tan ^ { - 1 } x = \tan ^ { - 1 } \frac { 1 } { 4 }$

Solve the equation for solutions over the interval $[ 0,2 \pi$ ). Write solutions as exact values or to four decimal places, as appropriate. - $\tan 3 x - \sec 3 x = 5$

Solve the equation in the interval [0°, 360°). Give solutions to the nearest tenth, if necessary. - $4 \sin ^ { 2 } \theta = 3$

Solve the equation for exact solutions. - $\cos ^ { - 1 } x = \sin ^ { - 1 } \frac { 5 } { 13 }$

Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree. - $\tan ^ { 2 } 2 \theta = 5$

Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree. - $\cos 2 \theta = \frac { \sqrt { 3 } } { 2 }$

Trigonometric Functions

Acute Angles and Right Triangles

Radian Measure and the Unit Circle

Graphs of the Circular Functions

Trigonometric Identities

Applications of Trigonometry and Vectors

Complex Numbers, Polar Equations, and Parametric Equations

Filters

Exam 6: Inverse Circular Functions and Trigonometric Equations

Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree. -tan 4ϴ = 0

Solve the equation in the interval [0°, 360°). Give solutions to the nearest tenth, if necessary. - 3sin⁡2θ−sin⁡θ−4=03 \sin ^ { 2 } \theta - \sin \theta - 4 = 03sin2θ−sinθ−4=0

Solve the equation for x, where x is restricted to the given interval. - y=cos⁡(x+12), for x in [−12,π−12]y = \cos ( x + 12 ) \text {, for } x \text { in } [ - 12 , \pi - 12 ]y=cos(x+12), for x in [−12,π−12]

Solve the equation for x, where x is restricted to the given interval. - 3y=tan⁡6x3 y = \tan 6 x3y=tan6x , for xxx in (−π12,π12)\left( - \frac { \pi } { 12 } , \frac { \pi } { 12 } \right)(−12π​,12π​)

Give the degree measure of . - θ=cot⁡−1(3)\theta = \cot ^ { - 1 } ( \sqrt { 3 } )θ=cot−1(3​)

Use a calculator to give the real number value. Round the answer to 7 decimal places. - y=cot⁡−1(2.5181552)y = \cot ^ { - 1 } ( 2.5181552 )y=cot−1(2.5181552)

Write the following as an algebraic expression in u, u > 0. - tan⁡(arcsec⁡u2+25u)\tan \left( \operatorname { arcsec } \frac { \sqrt { \mathrm { u } ^ { 2 } + 25 } } { \mathrm { u } } \right)tan(arcsecuu2+25​​)

Solve the equation in the interval [0°, 360°). Give solutions to the nearest tenth, if necessary. - csc⁡θ=1+cot⁡θ\csc \theta = 1 + \cot \thetacscθ=1+cotθ

Solve the equation for x, where x is restricted to the given interval. - y=4cot⁡x2, for x in (0,2π)y = 4 \cot \frac { x } { 2 } , \text { for } x \text { in } ( 0,2 \pi )y=4cot2x​, for x in (0,2π)

Give the exact value of the expression. - sin⁡(arctan⁡2)\sin ( \arctan 2 )sin(arctan2)

Solve the equation for exact solutions. - tan⁡−1(x+2)+tan⁡−1x=tan⁡−114\tan ^ { - 1 } ( x + 2 ) + \tan ^ { - 1 } x = \tan ^ { - 1 } \frac { 1 } { 4 }tan−1(x+2)+tan−1x=tan−141​

Solve the equation for solutions over the interval [0,2π[ 0,2 \pi[0,2π ). Write solutions as exact values or to four decimal places, as appropriate. - tan⁡3x−sec⁡3x=5\tan 3 x - \sec 3 x = 5tan3x−sec3x=5

Solve the equation in the interval [0°, 360°). Give solutions to the nearest tenth, if necessary. - 4sin⁡2θ=34 \sin ^ { 2 } \theta = 34sin2θ=3

Solve the equation for exact solutions. - cos⁡−1x=sin⁡−1513\cos ^ { - 1 } x = \sin ^ { - 1 } \frac { 5 } { 13 }cos−1x=sin−1135​

Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree. - tan⁡22θ=5\tan ^ { 2 } 2 \theta = 5tan22θ=5

Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree. - cos⁡2θ=32\cos 2 \theta = \frac { \sqrt { 3 } } { 2 }cos2θ=23​​