Find the missing parts of the triangle. -\[\begin{array} { l } \mathrm { A } = 10.5 ^ { \circ } \\ \mathrm { a } = 149 \mathrm { ft } \\ \mathrm { b } = 176 \mathrm { ft } \end{array}\] If necessary, round angles to the nearest tenth and side lengths to the nearest foot.

A) $\mathrm { B } _ { 1 } = 12.4 ^ { \circ } , \mathrm { C } _ { 1 } = 157.1 ^ { \circ } , \mathrm { c } _ { 1 } = 318 \mathrm { ft }$ B) $\mathrm { B } = 12.4 ^ { \circ } , \mathrm { C } = 157.1 ^ { \circ } , \mathrm { c } = 318 \mathrm { ft }$ $B _ { 2 } = 167.6 ^ { \circ } , C _ { 2 } = 1.9 ^ { \circ } , c _ { 2 } = 27 \mathrm { ft }$ C) no such triangle D) $\begin{array}{l} B_{1}=157.1^{\circ}, C_{1}=12.4^{\circ}, \mathrm{c}_{1}=318 \mathrm{f} \\ B_{2}=1.9^{\circ}, C_{2}=167.6^{\circ}, \mathrm{c}_{2}=27 \mathrm{ft} \end{array}$ A) $\mathrm { B } _ { 1 } = 12.4 ^ { \circ } , \mathrm { C } _ { 1 } = 157.1 ^ { \circ } , \mathrm { c } _ { 1 } = 318 \mathrm { ft }$ B) $\mathrm { B } = 12.4 ^ { \circ } , \mathrm { C } = 157.1 ^ { \circ } , \mathrm { c } = 318 \mathrm { ft }$ $B _ { 2 } = 167.6 ^ { \circ } , C _ { 2 } = 1.9 ^ { \circ } , c _ { 2 } = 27 \mathrm { ft }$ C) no such triangle D) $\begin{array}{l} B_{1}=157.1^{\circ}, C_{1}=12.4^{\circ}, \mathrm{c}_{1}=318 \mathrm{f} \\ B_{2}=1.9^{\circ}, C_{2}=167.6^{\circ}, \mathrm{c}_{2}=27 \mathrm{ft} \end{array}$

Find the missing parts of the triangle. -\[\begin{array} { l } \mathrm { B } = 40.1 ^ { \circ } \\ \mathrm { b } = 24.1 \mathrm { in } . \\ \mathrm { c } = 19.4 \mathrm { in } . \end{array}\] If necessary, round angles and side lengths to the nearest tenth.

A) $\mathrm { A } = 98.7 ^ { \circ } , \mathrm { C } = 41.2 ^ { \circ } , \mathrm { a } = 35.4 \mathrm { in }$. B) no such triangle C) $\mathrm { A } = 108.7 ^ { \circ } , \mathrm { C } = 31.2 ^ { \circ } , \mathrm { a } = 35.4 \mathrm { in }$. D) $\mathrm { A } = 31.2 ^ { \circ } , \mathrm { C } = 108.7 ^ { \circ } , \mathrm { a } = 35.4 \mathrm { in }$. A) $\mathrm { A } = 98.7 ^ { \circ } , \mathrm { C } = 41.2 ^ { \circ } , \mathrm { a } = 35.4 \mathrm { in }$. B) no such triangle C) $\mathrm { A } = 108.7 ^ { \circ } , \mathrm { C } = 31.2 ^ { \circ } , \mathrm { a } = 35.4 \mathrm { in }$. D) $\mathrm { A } = 31.2 ^ { \circ } , \mathrm { C } = 108.7 ^ { \circ } , \mathrm { a } = 35.4 \mathrm { in }$.

Exam 9: Applications of Trigonometry

Graph the polar equation for $\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$ - $r = 8 \sin 3 \theta \sin 4 \theta$ $Graph the polar equation for \theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right) - r = 8 \sin 3 \theta \sin 4 \theta$

(Multiple Choice)

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Question 201

Find the angle between the pair of vectors to the nearest tenth of a degree. -7i - 4j, 9i - 8j

(Multiple Choice)

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Question 202

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. -

(Multiple Choice)

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Question 203

Draw a sketch to represent the vector. Refer to the vectors pictured here. - $a + d$

(Multiple Choice)

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Question 204

Find the missing parts of the triangle. - =10. =149 =176 If necessary, round angles to the nearest tenth and side lengths to the nearest foot.

(Multiple Choice)

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Question 205

Find an equivalent equation in rectangular coordinates. - $r = 2 ( \sin \theta - \cos \theta )$

(Multiple Choice)

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Question 206

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. -A box weighing $77 \mathrm { lb }$ is hanging from the end of a rope. The box is pulled sideways by a horizontal rope with a force of $28 \mathrm { lb }$ . What angle, to the nearest degree, does the first rope make with the vertical?

(Multiple Choice)

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Question 207

The rectangular coordinates of a point are given. Express the point in polar coordinates with $r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$ - $( 0 , \sqrt { 7 } )$

(Multiple Choice)

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Question 208

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 2 } - i = 0$

(Multiple Choice)

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Question 209

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in $\left[ 0,360 ^ { \circ } \right]$ - $\langle - 3,0 \rangle$

(Multiple Choice)

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Question 210

The rectangular coordinates of a point are given. Express the point in polar coordinates with $r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$ - $( 4,4 )$

(Multiple Choice)

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Question 211

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal places. - $\left[ 8 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right) \right] \left[ 3 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right) \right]$

(Multiple Choice)

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Question 212

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $x = \sin t , y = \cos t ; t = \pi$

(Multiple Choice)

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Question 213

Find the missing parts of the triangle. - =40. =24.1. =19.4. If necessary, round angles and side lengths to the nearest tenth.

(Multiple Choice)

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Question 214

Find the given power. Write answer in rectangular form. - $\left[ 3 \operatorname { cis } 15 ^ { \circ } \right] ^ { 4 }$

(Multiple Choice)

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Question 215

Graph the polar equation for $\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$ - $r = 4 ( \cos \theta + \cos 2 \theta )$ $Graph the polar equation for \theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right) - r = 4 ( \cos \theta + \cos 2 \theta )$

(Multiple Choice)

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Question 216

Write the complex number in rectangular form. - $\operatorname { cis } 210$

(Multiple Choice)

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Question 217

Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth. -

(Multiple Choice)

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Question 218

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in $\left[ 0,360 ^ { \circ } \right]$ - $\langle 0 , - 18 \rangle$

(Multiple Choice)

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Question 219

Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth. -

(Multiple Choice)

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Question 220

Graph the polar equation for $\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$ - $r = 8 \sin 3 \theta \sin 4 \theta$ $Graph the polar equation for \theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right) - r = 8 \sin 3 \theta \sin 4 \theta$

Find the angle between the pair of vectors to the nearest tenth of a degree. -7i - 4j, 9i - 8j

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. -

Draw a sketch to represent the vector. Refer to the vectors pictured here. - $a + d$

Find the missing parts of the triangle. - =10. =149 =176 If necessary, round angles to the nearest tenth and side lengths to the nearest foot.

Find an equivalent equation in rectangular coordinates. - $r = 2 ( \sin \theta - \cos \theta )$

The rectangular coordinates of a point are given. Express the point in polar coordinates with $r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$ - $( 0 , \sqrt { 7 } )$

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 2 } - i = 0$

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in $\left[ 0,360 ^ { \circ } \right]$ - $\langle - 3,0 \rangle$

The rectangular coordinates of a point are given. Express the point in polar coordinates with $r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$ - $( 4,4 )$

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal places. - $\left[ 8 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right) \right] \left[ 3 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right) \right]$

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $x = \sin t , y = \cos t ; t = \pi$

Find the missing parts of the triangle. - =40. =24.1. =19.4. If necessary, round angles and side lengths to the nearest tenth.

Find the given power. Write answer in rectangular form. - $\left[ 3 \operatorname { cis } 15 ^ { \circ } \right] ^ { 4 }$

Graph the polar equation for $\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$ - $r = 4 ( \cos \theta + \cos 2 \theta )$ $Graph the polar equation for \theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right) - r = 4 ( \cos \theta + \cos 2 \theta )$

Write the complex number in rectangular form. - $\operatorname { cis } 210$

Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth. -

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in $\left[ 0,360 ^ { \circ } \right]$ - $\langle 0 , - 18 \rangle$

Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth. -

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 9: Applications of Trigonometry

Graph the polar equation for θ in [0∘,360∘)\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)θ in [0∘,360∘) - r=8sin⁡3θsin⁡4θr = 8 \sin 3 \theta \sin 4 \thetar=8sin3θsin4θ

Find the angle between the pair of vectors to the nearest tenth of a degree. -7i - 4j, 9i - 8j

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. -

Draw a sketch to represent the vector. Refer to the vectors pictured here. - a+da + da+d

Find the missing parts of the triangle. - =10. =149 =176 If necessary, round angles to the nearest tenth and side lengths to the nearest foot.

Find an equivalent equation in rectangular coordinates. - r=2(sin⁡θ−cos⁡θ)r = 2 ( \sin \theta - \cos \theta )r=2(sinθ−cosθ)

The rectangular coordinates of a point are given. Express the point in polar coordinates with r≥0 and 0∘≤θ<360∘. r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }r≥0 and 0∘≤θ<360∘. - (0,7)( 0 , \sqrt { 7 } )(0,7​)

Find all solutions of the equation. Leave answers in trigonometric form. - x2−i=0x ^ { 2 } - i = 0x2−i=0

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360∘]\left[ 0,360 ^ { \circ } \right][0,360∘] - ⟨−3,0⟩\langle - 3,0 \rangle⟨−3,0⟩

The rectangular coordinates of a point are given. Express the point in polar coordinates with r≥0 and 0∘≤θ<360∘. r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }r≥0 and 0∘≤θ<360∘. - (4,4)( 4,4 )(4,4)

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - x=sin⁡t,y=cos⁡t;t=πx = \sin t , y = \cos t ; t = \pix=sint,y=cost;t=π

Find the missing parts of the triangle. - =40. =24.1. =19.4. If necessary, round angles and side lengths to the nearest tenth.

Find the given power. Write answer in rectangular form. - [3cis⁡15∘]4\left[ 3 \operatorname { cis } 15 ^ { \circ } \right] ^ { 4 }[3cis15∘]4

Graph the polar equation for θ in [0∘,360∘)\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)θ in [0∘,360∘) - r=4(cos⁡θ+cos⁡2θ)r = 4 ( \cos \theta + \cos 2 \theta )r=4(cosθ+cos2θ)

Write the complex number in rectangular form. - cis⁡210\operatorname { cis } 210cis210

Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth. -

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360∘]\left[ 0,360 ^ { \circ } \right][0,360∘] - ⟨0,−18⟩\langle 0 , - 18 \rangle⟨0,−18⟩

Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth. -

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Graph the polar equation for $\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$ - $r = 8 \sin 3 \theta \sin 4 \theta$ $Graph the polar equation for \theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right) - r = 8 \sin 3 \theta \sin 4 \theta$

Draw a sketch to represent the vector. Refer to the vectors pictured here. - $a + d$

Find an equivalent equation in rectangular coordinates. - $r = 2 ( \sin \theta - \cos \theta )$

The rectangular coordinates of a point are given. Express the point in polar coordinates with $r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$ - $( 0 , \sqrt { 7 } )$

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 2 } - i = 0$

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in $\left[ 0,360 ^ { \circ } \right]$ - $\langle - 3,0 \rangle$

The rectangular coordinates of a point are given. Express the point in polar coordinates with $r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$ - $( 4,4 )$

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $x = \sin t , y = \cos t ; t = \pi$

Find the given power. Write answer in rectangular form. - $\left[ 3 \operatorname { cis } 15 ^ { \circ } \right] ^ { 4 }$

Graph the polar equation for $\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$ - $r = 4 ( \cos \theta + \cos 2 \theta )$ $Graph the polar equation for \theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right) - r = 4 ( \cos \theta + \cos 2 \theta )$

Write the complex number in rectangular form. - $\operatorname { cis } 210$

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in $\left[ 0,360 ^ { \circ } \right]$ - $\langle 0 , - 18 \rangle$