Question 1

Write the following as an algebraic expression in u, u > 0.
-$\sin \left( \arcsin \frac { \mathrm { u } } { \sqrt { 3 } } \right)$

Accepted Answer

A)  $\frac { \mathrm { u } \sqrt { 3 } } { 3 }$ 
B)  $\frac { u \sqrt { u ^ { 2 } - 3 } } { u ^ { 2 } - 3 }$ 
C)  $\frac { \sqrt { u ^ { 2 } + 3 } } { u ^ { 2 } + 3 }$ 
D)  $\mathrm { u } \sqrt { 3 }$ 
A)  $\frac { \mathrm { u } \sqrt { 3 } } { 3 }$ 
B)  $\frac { u \sqrt { u ^ { 2 } - 3 } } { u ^ { 2 } - 3 }$ 
C)  $\frac { \sqrt { u ^ { 2 } + 3 } } { u ^ { 2 } + 3 }$ 
D)  $\mathrm { u } \sqrt { 3 }$

Question 2

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 $y = \sec x$ sketch the graph of $y = \sec ^ { - 1 } x$ as defined in the text. Give the domain and the range.

Accepted Answer

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

Question 3

Use a calculator to give the value to the nearest degree.
-$$\theta = \sin ^ { - 1 } ( 0.6561 )$$

Accepted Answer

A)  $41 ^ { \circ }$ 
B)  $- 41 ^ { \circ }$ 
C)  $44 ^ { \circ }$ 
D)  $39 ^ { \circ }$ 
A)  $41 ^ { \circ }$ 
B)  $- 41 ^ { \circ }$ 
C)  $44 ^ { \circ }$ 
D)  $39 ^ { \circ }$

Question 4

Solve the equation for exact solutions.
-$6 \cos ^ { - 1 } x = \pi$

Accepted Answer

A)  $\left\{ \frac { \sqrt { 2 } } { 2 } \right\}$ 
B)  $\left\{ \frac { \pi } { 6 } \right\}$ 
C)  $\left\{ \frac { 1 } { 2 } \right\}$ 
D)  $\left\{ \frac { \sqrt { 3 } } { 2 } \right\}$ 
A)  $\left\{ \frac { \sqrt { 2 } } { 2 } \right\}$ 
B)  $\left\{ \frac { \pi } { 6 } \right\}$ 
C)  $\left\{ \frac { 1 } { 2 } \right\}$ 
D)  $\left\{ \frac { \sqrt { 3 } } { 2 } \right\}$

Question 5

Use a calculator to find the value. Give answers as real numbers and round to 4 decimal places, if necessary.
-sin (arctan 2)

Accepted Answer

A) Undefined 
B) 0.8944 
C) -0.8172 
D) 0 
A) Undefined 
B) 0.8944 
C) -0.8172 
D) 0

Question 6

Solve the equation (x in radians and in degrees) for all exact solutions where appropriate. Round approximate answers
in radians to four decimal places and approximate answers in degrees to the nearest tenth.
-$$\frac { 4 \tan \theta } { 5 - \tan ^ { 2 } \theta } = 1$$

Accepted Answer

A)  $\varnothing$ 
B)  $\left\{ 0 ^ { \circ } + 180 ^ { \circ } \mathrm { n } , 45 ^ { \circ } + 180 ^ { \circ } \mathrm { n } , 101.3 ^ { \circ } + 180 ^ { \circ } \mathrm { n } \right\}$ 
C)  $\left\{ 45 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 101.3 ^ { \circ } + 360 ^ { \circ } \mathrm { n } \right\}$ 
D)  $\left\{ 45 ^ { \circ } + 180 ^ { \circ } \mathrm { n } , 101.3 ^ { \circ } + 180 ^ { \circ } \mathrm { n } \right\}$ 
A)  $\varnothing$ 
B)  $\left\{ 0 ^ { \circ } + 180 ^ { \circ } \mathrm { n } , 45 ^ { \circ } + 180 ^ { \circ } \mathrm { n } , 101.3 ^ { \circ } + 180 ^ { \circ } \mathrm { n } \right\}$ 
C)  $\left\{ 45 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 101.3 ^ { \circ } + 360 ^ { \circ } \mathrm { n } \right\}$ 
D)  $\left\{ 45 ^ { \circ } + 180 ^ { \circ } \mathrm { n } , 101.3 ^ { \circ } + 180 ^ { \circ } \mathrm { n } \right\}$

Question 7

Use a calculator to give the real number value. Round the answer to 7 decimal places.
-$$y = \sin ^ { - 1 } ( 0.6561 )$$

Accepted Answer

A)  $0.6809524$ 
B)  $0.5806515$ 
C)  $- 0.7158730$ 
D)  $0.7156393$ 
A)  $0.6809524$ 
B)  $0.5806515$ 
C)  $- 0.7158730$ 
D)  $0.7156393$

Question 8

Use a calculator to give the value to the nearest degree.
-$$\theta = \sin ^ { - 1 } ( - 0.4848 )$$

Accepted Answer

A)  $- 29 ^ { \circ }$ 
B)  $- 31 ^ { \circ }$ 
C)  $- 28 ^ { \circ }$ 
D)  $151 ^ { \circ }$ 
A)  $- 29 ^ { \circ }$ 
B)  $- 31 ^ { \circ }$ 
C)  $- 28 ^ { \circ }$ 
D)  $151 ^ { \circ }$

Question 9

Solve the equation for x, where x is restricted to the given interval.
-$y = 8 \cos 3 x$, for $x$ in $\left[ 0 , \frac { \pi } { 3 } \right]$

Accepted Answer

A)  $x = 3 \arccos \frac { y } { 8 }$ 
B)  $x = 8 \arccos \frac { y } { 3 }$ 
C)  $x = \frac { 1 } { 8 } \arccos \frac { y } { 3 }$ 
D)  $x = \frac { 1 } { 3 } \arccos \frac { y } { 8 }$ 
A)  $x = 3 \arccos \frac { y } { 8 }$ 
B)  $x = 8 \arccos \frac { y } { 3 }$ 
C)  $x = \frac { 1 } { 8 } \arccos \frac { y } { 3 }$ 
D)  $x = \frac { 1 } { 3 } \arccos \frac { y } { 8 }$

Question 10

Find the exact value of the real number y.
-$y = \tan ^ { - 1 } ( - 1 )$

Accepted Answer

A)  $\frac { 5 \pi } { 4 }$ 
B)  $\frac { 7 \pi } { 4 }$ 
C)  $\frac { 3 \pi } { 4 }$ 
D)  $\frac { \pi } { 4 }$ 
A)  $\frac { 5 \pi } { 4 }$ 
B)  $\frac { 7 \pi } { 4 }$ 
C)  $\frac { 3 \pi } { 4 }$ 
D)  $\frac { \pi } { 4 }$

Question 11

Give the degree measure of .
-$$\theta = \arctan \left( \frac { \sqrt { 3 } } { 3 } \right)$$

Accepted Answer

A)  $- 30 ^ { \circ }$ 
B)  $330 ^ { \circ }$ 
C)  $150 ^ { \circ }$ 
D)  $30 ^ { \circ }$ 
A)  $- 30 ^ { \circ }$ 
B)  $330 ^ { \circ }$ 
C)  $150 ^ { \circ }$ 
D)  $30 ^ { \circ }$

Question 12

Solve the equation for exact solutions.
-$\arctan x = \operatorname { arccot } \frac { 8 } { 11 }$

Accepted Answer

A)  $\left\{ \frac { 8 } { 11 } \right\}$ 
B)  $\varnothing$ 
C)  $\{ 0 \}$ 
D)  $\left\{ \frac { 11 } { 8 } \right\}$ 
A)  $\left\{ \frac { 8 } { 11 } \right\}$ 
B)  $\varnothing$ 
C)  $\{ 0 \}$ 
D)  $\left\{ \frac { 11 } { 8 } \right\}$

Question 13

Find the exact value of the real number y.
-$$y = \sin ^ { - 1 } \left( \frac { \sqrt { 3 } } { 2 } \right)$$

Accepted Answer

A)  $\frac { \pi } { 3 }$ 
B)  $\frac { \pi } { 4 }$ 
C)  $\frac { 2 \pi } { 3 }$ 
D)  $\frac { 3 \pi } { 4 }$ 
A)  $\frac { \pi } { 3 }$ 
B)  $\frac { \pi } { 4 }$ 
C)  $\frac { 2 \pi } { 3 }$ 
D)  $\frac { 3 \pi } { 4 }$

Question 14

Solve the problem.
-In an electric circuit, the electromotive force is defined as $V = \cos 2 \pi t$, where $t$ is time in seconds. Solve the equation for $\mathrm { t }$.

Accepted Answer

A)  $t = \frac { 1 } { 2 \pi } \cos V$ 
B)  $t = 2 \pi \cos V$ 
C)  $t = \frac { 1 } { 2 \pi } \arccos V$ 
D)  $t = 2 \pi \arccos V$ 
A)  $t = \frac { 1 } { 2 \pi } \cos V$ 
B)  $t = 2 \pi \cos V$ 
C)  $t = \frac { 1 } { 2 \pi } \arccos V$ 
D)  $t = 2 \pi \arccos V$

Question 15

Use a calculator to find the value. Give answers as real numbers and round to 4 decimal places, if necessary.
-$\tan ( \arcsin 2 )$

Accepted Answer

A)  $0.8944$ 
B)  Undefined 
C)  0 
D)  $- 0.8172$ 
A)  $0.8944$ 
B)  Undefined 
C)  0 
D)  $- 0.8172$

Question 16

Graph the inverse circular function.
-$$y = \operatorname { arccsc } \frac { 1 } { 2 } x$$

Accepted Answer

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

Question 17

Solve the equation for exact solutions over the interval [0, 2 $$[ 0,2 \pi ) .$$
-$\cos ^ { 2 } x + 2 \cos x + 1 = 0$

Accepted Answer

A)  $\left\{ \frac { \pi } { 4 } , \frac { 7 \pi } { 4 } \right\}$ 
B)  $\left\{ \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } \right\}$ 
C)  $\{ \pi \}$ 
D)  $\{ 2 \pi \}$ 
A)  $\left\{ \frac { \pi } { 4 } , \frac { 7 \pi } { 4 } \right\}$ 
B)  $\left\{ \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } \right\}$ 
C)  $\{ \pi \}$ 
D)  $\{ 2 \pi \}$

Question 18

Solve the problem.
-In the study of alternating electric current, capacitive voltage is given by $$\mathrm { V } _ { \mathrm { C } } = - \frac { \mathrm { i } } { 2 \pi \mathrm { f } } \cos 2 \pi \mathrm { ft } \text {, }$$
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 $t$.

Accepted Answer

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

Question 19

Graph the inverse circular function.
-$y=\tan ^{-1} x$

Accepted Answer

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

Question 20

Find the exact value of the real number y.
-$$y = \cos ^ { - 1 } \left( \frac { \sqrt { 3 } } { 2 } \right)$$

Accepted Answer

A)  $\frac { 7 \pi } { 4 }$ 
B)  $\frac { \pi } { 4 }$ 
C)  $\frac { \pi } { 6 }$ 
D)  $\frac { 11 \pi } { 6 }$ 
A)  $\frac { 7 \pi } { 4 }$ 
B)  $\frac { \pi } { 4 }$ 
C)  $\frac { \pi } { 6 }$ 
D)  $\frac { 11 \pi } { 6 }$

Write the following as an algebraic expression in u, u > 0. - $\sin \left( \arcsin \frac { \mathrm { u } } { \sqrt { 3 } } \right)$

Use a calculator to give the value to the nearest degree. - $\theta = \sin ^ { - 1 } ( 0.6561 )$

Solve the equation for exact solutions. - $6 \cos ^ { - 1 } x = \pi$

Use a calculator to find the value. Give answers as real numbers and round to 4 decimal places, if necessary. -sin (arctan 2)

Solve the equation (x in radians and in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. - $\frac { 4 \tan \theta } { 5 - \tan ^ { 2 } \theta } = 1$

Use a calculator to give the real number value. Round the answer to 7 decimal places. - $y = \sin ^ { - 1 } ( 0.6561 )$

Use a calculator to give the value to the nearest degree. - $\theta = \sin ^ { - 1 } ( - 0.4848 )$

Solve the equation for x, where x is restricted to the given interval. - $y = 8 \cos 3 x$ , for $x$ in $\left[ 0 , \frac { \pi } { 3 } \right]$

Find the exact value of the real number y. - $y = \tan ^ { - 1 } ( - 1 )$

Give the degree measure of . - $\theta = \arctan \left( \frac { \sqrt { 3 } } { 3 } \right)$

Solve the equation for exact solutions. - $\arctan x = \operatorname { arccot } \frac { 8 } { 11 }$

Find the exact value of the real number y. - $y = \sin ^ { - 1 } \left( \frac { \sqrt { 3 } } { 2 } \right)$

Solve the problem. -In an electric circuit, the electromotive force is defined as $V = \cos 2 \pi t$ , where $t$ is time in seconds. Solve the equation for $\mathrm { t }$ .

Use a calculator to find the value. Give answers as real numbers and round to 4 decimal places, if necessary. - $\tan ( \arcsin 2 )$

Graph the inverse circular function. - $y = \operatorname { arccsc } \frac { 1 } { 2 } x$ $Graph the inverse circular function. - y = \operatorname { arccsc } \frac { 1 } { 2 } x$

Solve the equation for exact solutions over the interval [0, 2 $[ 0,2 \pi ) .$ - $\cos ^ { 2 } x + 2 \cos x + 1 = 0$

Graph the inverse circular function. - $y=\tan ^{-1} x$ $Graph the inverse circular function. - y=\tan ^{-1} x$

Find the exact value of the real number y. - $y = \cos ^ { - 1 } \left( \frac { \sqrt { 3 } } { 2 } \right)$

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

Write the following as an algebraic expression in u, u > 0. - sin⁡(arcsin⁡u3)\sin \left( \arcsin \frac { \mathrm { u } } { \sqrt { 3 } } \right)sin(arcsin3​u​)

Use a calculator to give the value to the nearest degree. - θ=sin⁡−1(0.6561)\theta = \sin ^ { - 1 } ( 0.6561 )θ=sin−1(0.6561)

Solve the equation for exact solutions. - 6cos⁡−1x=π6 \cos ^ { - 1 } x = \pi6cos−1x=π

Use a calculator to find the value. Give answers as real numbers and round to 4 decimal places, if necessary. -sin (arctan 2)

Use a calculator to give the real number value. Round the answer to 7 decimal places. - y=sin⁡−1(0.6561)y = \sin ^ { - 1 } ( 0.6561 )y=sin−1(0.6561)

Use a calculator to give the value to the nearest degree. - θ=sin⁡−1(−0.4848)\theta = \sin ^ { - 1 } ( - 0.4848 )θ=sin−1(−0.4848)

Solve the equation for x, where x is restricted to the given interval. - y=8cos⁡3xy = 8 \cos 3 xy=8cos3x , for xxx in [0,π3]\left[ 0 , \frac { \pi } { 3 } \right][0,3π​]

Find the exact value of the real number y. - y=tan⁡−1(−1)y = \tan ^ { - 1 } ( - 1 )y=tan−1(−1)

Give the degree measure of . - θ=arctan⁡(33)\theta = \arctan \left( \frac { \sqrt { 3 } } { 3 } \right)θ=arctan(33​​)

Solve the equation for exact solutions. - arctan⁡x=arccot⁡811\arctan x = \operatorname { arccot } \frac { 8 } { 11 }arctanx=arccot118​

Find the exact value of the real number y. - y=sin⁡−1(32)y = \sin ^ { - 1 } \left( \frac { \sqrt { 3 } } { 2 } \right)y=sin−1(23​​)

Solve the problem. -In an electric circuit, the electromotive force is defined as V=cos⁡2πtV = \cos 2 \pi tV=cos2πt , where ttt is time in seconds. Solve the equation for t\mathrm { t }t .

Use a calculator to find the value. Give answers as real numbers and round to 4 decimal places, if necessary. - tan⁡(arcsin⁡2)\tan ( \arcsin 2 )tan(arcsin2)

Graph the inverse circular function. - y=arccsc⁡12xy = \operatorname { arccsc } \frac { 1 } { 2 } xy=arccsc21​x

Solve the equation for exact solutions over the interval [0, 2 [0,2π).[ 0,2 \pi ) .[0,2π). - cos⁡2x+2cos⁡x+1=0\cos ^ { 2 } x + 2 \cos x + 1 = 0cos2x+2cosx+1=0

Graph the inverse circular function. - y=tan⁡−1xy=\tan ^{-1} xy=tan−1x

Find the exact value of the real number y. - y=cos⁡−1(32)y = \cos ^ { - 1 } \left( \frac { \sqrt { 3 } } { 2 } \right)y=cos−1(23​​)