Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. -\[\begin{array} { l } A = 22 ^ { \circ } 10 ^ { \prime } \\ B = 26 ^ { \circ } 20 ^ { \prime } \\ a = 11.2 \end{array}\]

A) $\mathrm { C } = 131 ^ { \circ } 30 ^ { \prime } , \mathrm { b } = 22.2 , \mathrm { c } = 13.2$ B) $\mathrm { C } = 131 ^ { \circ } 30 ^ { \prime } , \mathrm { b } = 13.2 , \mathrm { c } = 22.2$ C) $\mathrm { C } = 132 ^ { \circ } 30 ^ { \prime } , \mathrm { b } = 22.2 , \mathrm { c } = 13.2$ D) $\mathrm { C } = 132 ^ { \circ } 30 ^ { \prime } , \mathrm { b } = 13.2 , \mathrm { c } = 22.2$ A) $\mathrm { C } = 131 ^ { \circ } 30 ^ { \prime } , \mathrm { b } = 22.2 , \mathrm { c } = 13.2$ B) $\mathrm { C } = 131 ^ { \circ } 30 ^ { \prime } , \mathrm { b } = 13.2 , \mathrm { c } = 22.2$ C) $\mathrm { C } = 132 ^ { \circ } 30 ^ { \prime } , \mathrm { b } = 22.2 , \mathrm { c } = 13.2$ D) $\mathrm { C } = 132 ^ { \circ } 30 ^ { \prime } , \mathrm { b } = 13.2 , \mathrm { c } = 22.2$

Exam 9: Applications of Trigonometry

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 25 \left( \cos 240 ^ { \circ } + \mathrm { i } \sin 240 ^ { \circ } \right) } { 5 \left( \cos 30 ^ { \circ } + \mathrm { i } \sin 30 ^ { \circ } \right) }$

(Multiple Choice)

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Question 101

Find the product. Write the product in rectangular form, using exact values. - $\left[ 4 \left( \cos 225 ^ { \circ } + \mathrm { i } \sin 225 ^ { \circ } \right) \right] \left[ 6 \left( \cos 225 ^ { \circ } + \mathrm { i } \sin 225 ^ { \circ } \right) \right]$

(Multiple Choice)

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Question 102

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides, by the law of sines. -a, c, and C

(Multiple Choice)

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Question 103

Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. - A=21 B=22 a=11.2

(Multiple Choice)

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Question 104

For the given rectangular equation, give its equivalent polar equation. - $4 x - 9 y = - 12$

(Multiple Choice)

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Question 105

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. -Starting at point $\mathrm { A }$ , a ship sails $57 \mathrm {~km}$ on a bearing of $186 ^ { \circ }$ , then turns and sails $35 \mathrm {~km}$ on a bearing of $303 ^ { \circ }$ . Find the distance of the ship from point $\mathrm { A }$ .

(Multiple Choice)

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Question 106

Find the given power. Write answer in rectangular form. - $( - 5 \sqrt { 2 } + 5 \sqrt { 2 } i ) ^ { 3 }$

(Multiple Choice)

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Question 107

Find the angle between the pair of vectors to the nearest tenth of a degree. -8i + 2j, -6i + 3j

(Multiple Choice)

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Question 108

Determine whether the pair of vectors is orthogonal. --4, -1 , -8, 32 1

(Multiple Choice)

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Question 109

Write the complex number in rectangular form. - $10.83 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$

(Multiple Choice)

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Question 110

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 pilot wants to fly on a bearing of $69.2 ^ { \circ }$ . By flying due east, he finds that a $56 - \mathrm { mph }$ wind, blowing from the south, puts him on course. Find the airspeed of the plane.

(Multiple Choice)

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Question 111

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in $\left[ 0,360 ^ { \circ } \right]$ - $\langle - 4 , - 3 \rangle$

(Multiple Choice)

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Question 112

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 2 } + 1 - \sqrt { 3 } i = 0$

(Multiple Choice)

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Question 113

Graph the complex number. - $-5-i$

(Multiple Choice)

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Question 114

Find an equivalent equation in rectangular coordinates. - $r ( \cos \theta - \sin \theta ) = 5$

(Multiple Choice)

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Question 115

Solve the problem. -Find the area of a triangular-shaped field with sides of $171.9 \mathrm {~m}$ and $192.8 \mathrm {~m}$ , and the included angle between them measuring $67.77 ^ { \circ }$ . Round to the nearest square meter.

(Multiple Choice)

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Question 116

Plot the point. - $\left(2,225^{\circ}\right)$ $Plot the point. - \left(2,225^{\circ}\right)$

(Multiple Choice)

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Question 117

Find the dot product for the pair of vectors. -1, 11, 7, 1

(Multiple Choice)

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Question 118

Write the complex number in rectangular form. - $3 \operatorname { cis } 240 ^ { \circ }$

(Multiple Choice)

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Question 119

Determine two pairs of polar coordinates for the point with $0 ^ { \circ } \leq \theta < 360 ^ { \circ }$ - $( 0 , \sqrt { 5 } )$

(Multiple Choice)

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Question 120

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 25 \left( \cos 240 ^ { \circ } + \mathrm { i } \sin 240 ^ { \circ } \right) } { 5 \left( \cos 30 ^ { \circ } + \mathrm { i } \sin 30 ^ { \circ } \right) }$

Find the product. Write the product in rectangular form, using exact values. - $\left[ 4 \left( \cos 225 ^ { \circ } + \mathrm { i } \sin 225 ^ { \circ } \right) \right] \left[ 6 \left( \cos 225 ^ { \circ } + \mathrm { i } \sin 225 ^ { \circ } \right) \right]$

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides, by the law of sines. -a, c, and C

Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. - A=21 B=22 a=11.2

For the given rectangular equation, give its equivalent polar equation. - $4 x - 9 y = - 12$

Find the given power. Write answer in rectangular form. - $( - 5 \sqrt { 2 } + 5 \sqrt { 2 } i ) ^ { 3 }$

Find the angle between the pair of vectors to the nearest tenth of a degree. -8i + 2j, -6i + 3j

Determine whether the pair of vectors is orthogonal. --4, -1 , -8, 32 1

Write the complex number in rectangular form. - $10.83 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in $\left[ 0,360 ^ { \circ } \right]$ - $\langle - 4 , - 3 \rangle$

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 2 } + 1 - \sqrt { 3 } i = 0$

Graph the complex number. - $-5-i$

Find an equivalent equation in rectangular coordinates. - $r ( \cos \theta - \sin \theta ) = 5$

Solve the problem. -Find the area of a triangular-shaped field with sides of $171.9 \mathrm {~m}$ and $192.8 \mathrm {~m}$ , and the included angle between them measuring $67.77 ^ { \circ }$ . Round to the nearest square meter.

Plot the point. - $\left(2,225^{\circ}\right)$ $Plot the point. - \left(2,225^{\circ}\right)$

Find the dot product for the pair of vectors. -1, 11, 7, 1

Write the complex number in rectangular form. - $3 \operatorname { cis } 240 ^ { \circ }$

Determine two pairs of polar coordinates for the point with $0 ^ { \circ } \leq \theta < 360 ^ { \circ }$ - $( 0 , \sqrt { 5 } )$

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

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides, by the law of sines. -a, c, and C

Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. - A=21 B=22 a=11.2

For the given rectangular equation, give its equivalent polar equation. - 4x−9y=−124 x - 9 y = - 124x−9y=−12

Find the given power. Write answer in rectangular form. - (−52+52i)3( - 5 \sqrt { 2 } + 5 \sqrt { 2 } i ) ^ { 3 }(−52​+52​i)3

Find the angle between the pair of vectors to the nearest tenth of a degree. -8i + 2j, -6i + 3j

Determine whether the pair of vectors is orthogonal. --4, -1 , -8, 32 1

Write the complex number in rectangular form. - 10.83(cos⁡30∘+isin⁡30∘)10.83 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)10.83(cos30∘+isin30∘)

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∘] - ⟨−4,−3⟩\langle - 4 , - 3 \rangle⟨−4,−3⟩

Find all solutions of the equation. Leave answers in trigonometric form. - x2+1−3i=0x ^ { 2 } + 1 - \sqrt { 3 } i = 0x2+1−3​i=0

Graph the complex number. - −5−i-5-i−5−i

Find an equivalent equation in rectangular coordinates. - r(cos⁡θ−sin⁡θ)=5r ( \cos \theta - \sin \theta ) = 5r(cosθ−sinθ)=5

Solve the problem. -Find the area of a triangular-shaped field with sides of 171.9 m171.9 \mathrm {~m}171.9 m and 192.8 m192.8 \mathrm {~m}192.8 m , and the included angle between them measuring 67.77∘67.77 ^ { \circ }67.77∘ . Round to the nearest square meter.

Plot the point. - (2,225∘)\left(2,225^{\circ}\right)(2,225∘)

Find the dot product for the pair of vectors. -1, 11, 7, 1

Write the complex number in rectangular form. - 3cis⁡240∘3 \operatorname { cis } 240 ^ { \circ }3cis240∘

Determine two pairs of polar coordinates for the point with 0∘≤θ<360∘0 ^ { \circ } \leq \theta < 360 ^ { \circ }0∘≤θ<360∘ - (0,5)( 0 , \sqrt { 5 } )(0,5​)

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

For the given rectangular equation, give its equivalent polar equation. - $4 x - 9 y = - 12$

Find the given power. Write answer in rectangular form. - $( - 5 \sqrt { 2 } + 5 \sqrt { 2 } i ) ^ { 3 }$

Write the complex number in rectangular form. - $10.83 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in $\left[ 0,360 ^ { \circ } \right]$ - $\langle - 4 , - 3 \rangle$

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 2 } + 1 - \sqrt { 3 } i = 0$

Graph the complex number. - $-5-i$

Find an equivalent equation in rectangular coordinates. - $r ( \cos \theta - \sin \theta ) = 5$

Solve the problem. -Find the area of a triangular-shaped field with sides of $171.9 \mathrm {~m}$ and $192.8 \mathrm {~m}$ , and the included angle between them measuring $67.77 ^ { \circ }$ . Round to the nearest square meter.

Plot the point. - $\left(2,225^{\circ}\right)$ $Plot the point. - \left(2,225^{\circ}\right)$

Write the complex number in rectangular form. - $3 \operatorname { cis } 240 ^ { \circ }$

Determine two pairs of polar coordinates for the point with $0 ^ { \circ } \leq \theta < 360 ^ { \circ }$ - $( 0 , \sqrt { 5 } )$