Find the missing parts of the triangle. -\[\begin{array} { l } \mathrm { A } = 76 ^ { \circ } \\ \mathrm { a } = 30 \mathrm { yd } \\ \mathrm { b } = 61 \mathrm { yd } \end{array}\] If necessary, round angles to the nearest degree and side lengths to the nearest yard.

A) $\mathrm { B } = 29 ^ { \circ } , \mathrm { C } = 75 ^ { \circ } , \mathrm { c } = 81 \mathrm { yd }$ B) no such triangle C) $\mathrm { B } = 29 ^ { \circ } , \mathrm { C } = 75 ^ { \circ } , \mathrm { c } = 75 \mathrm { yd }$ D) $\mathrm { B } = 75 ^ { \circ } , \mathrm { C } = 29 ^ { \circ } , \mathrm { c } = 79 \mathrm { yd }$ A) $\mathrm { B } = 29 ^ { \circ } , \mathrm { C } = 75 ^ { \circ } , \mathrm { c } = 81 \mathrm { yd }$ B) no such triangle C) $\mathrm { B } = 29 ^ { \circ } , \mathrm { C } = 75 ^ { \circ } , \mathrm { c } = 75 \mathrm { yd }$ D) $\mathrm { B } = 75 ^ { \circ } , \mathrm { C } = 29 ^ { \circ } , \mathrm { c } = 79 \mathrm { yd }$

Find the missing parts of the triangle. -\[\begin{array} { l } \mathrm { A } = 30 ^ { \circ } \\ \mathrm { a } = 5.95 \\ \mathrm {~b} = 11.9 \end{array}\] If necessary, round angles to the nearest degree and side lengths to the nearest hundredth.

A) $B = 60 ^ { \circ } , C = 90 ^ { \circ } , \mathrm { c } = 10.31$ B) $\mathrm { B } = 60 ^ { \circ } , \mathrm { C } = 60 ^ { \circ } , \mathrm { c } = 10.31$ C) $B = 90 ^ { \circ } , C = 60 ^ { \circ } , \mathrm { c } = 10.31$ D) no such triangle A) $B = 60 ^ { \circ } , C = 90 ^ { \circ } , \mathrm { c } = 10.31$ B) $\mathrm { B } = 60 ^ { \circ } , \mathrm { C } = 60 ^ { \circ } , \mathrm { c } = 10.31$ C) $B = 90 ^ { \circ } , C = 60 ^ { \circ } , \mathrm { c } = 10.31$ D) no such triangle

Exam 8: Applications of Trigonometry

Solve. -A complex number z does not belong to the Mandelbrot set if any of the complex numbers in the sequence $z , z ^ { 2 } + z , \left( z ^ { 2 } + z \right) ^ { 2 } + z , \left[ \left( z ^ { 2 } + z \right) ^ { 2 } + z \right] ^ { 2 } + z , \ldots$ has modulus exceeding 2 . Does $\mathrm { z } = 0.6 - 0.7 \mathrm { i }$ belong to the Mandelbrot set?

(Multiple Choice)

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Question 221

Give two parametric representations for the equation of the parabola. - $y = ( x + 1 ) ^ { 2 } - 8$

(Multiple Choice)

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Question 222

Find an equivalent equation in rectangular coordinates. - $\mathrm { r } = \frac { 5 } { 1 + \cos \theta }$

(Multiple Choice)

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Question 223

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { \sqrt { 3 } ( \cos 315 + i \sin 315 ) } { \sqrt { 6 } ( \cos 45 + i \sin 45 ) }$

(Multiple Choice)

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Question 224

Answer the question. -If $\mathrm { n }$ is an even number, then which of the following statements is true?

(Multiple Choice)

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Question 225

Solve the problem. -Two points $A$ and $B$ are on opposite sides of a building. A surveyor chooses a third point $C 64$ yd from $B$ and 93 yd from $A$ , with angle $A C B$ measuring $67.3 ^ { \circ }$ . How far apart are $A$ and $B$ (to the nearest yard)?

(Multiple Choice)

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Question 226

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - $( 4 , - 4 )$

(Multiple Choice)

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Question 227

Answer the question. -In which quadrants do the square roots of i lie?

(Multiple Choice)

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Question 228

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle - 2,8 \rangle , \mathbf { v } = \langle - 9 , - 6 \rangle$ . Find $\mathbf { u } + \mathbf { v }$ .

(Multiple Choice)

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Question 229

Find the indicated angle or side. Give an exact answer. -Find the measure of angle A in degrees.

(Multiple Choice)

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Question 230

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - $( - 6,2 \sqrt { 3 } )$

(Multiple Choice)

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Question 231

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve. -

(Multiple Choice)

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Question 232

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

(Multiple Choice)

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Question 233

Determine whether the pair of vectors is orthogonal. - $\langle - 3 , \sqrt { 3 } \rangle , \langle - 2 \sqrt { 3 } , - 6 \rangle$

(Multiple Choice)

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Question 234

Give the rectangular coordinates for the point. - $\left( - 5,330 ^ { \circ } \right)$

(Multiple Choice)

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Question 235

Find the missing parts of the triangle. - =7 =30 =61 If necessary, round angles to the nearest degree and side lengths to the nearest yard.

(Multiple Choice)

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Question 236

Find the missing parts of the triangle. - =3 =5.95 =11.9 If necessary, round angles to the nearest degree and side lengths to the nearest hundredth.

(Multiple Choice)

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Question 237

Find all specified roots. -Eighth roots of $i$ .

(Multiple Choice)

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Question 238

Find all solutions of the equation. Leave answers in trigonometric form. - $\mathrm { x } ^ { 3 } + 8 = 0$

(Multiple Choice)

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Question 239

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve. - $x = 2 \tan t , y = 5 \sec t$ , for $t$ in $[ 0,2 \pi ]$ $Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve. - x = 2 \tan t , y = 5 \sec t , for t in [ 0,2 \pi ]$

(Multiple Choice)

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Question 240

Give two parametric representations for the equation of the parabola. - $y = ( x + 1 ) ^ { 2 } - 8$

Find an equivalent equation in rectangular coordinates. - $\mathrm { r } = \frac { 5 } { 1 + \cos \theta }$

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { \sqrt { 3 } ( \cos 315 + i \sin 315 ) } { \sqrt { 6 } ( \cos 45 + i \sin 45 ) }$

Answer the question. -If $\mathrm { n }$ is an even number, then which of the following statements is true?

Solve the problem. -Two points $A$ and $B$ are on opposite sides of a building. A surveyor chooses a third point $C 64$ yd from $B$ and 93 yd from $A$ , with angle $A C B$ measuring $67.3 ^ { \circ }$ . How far apart are $A$ and $B$ (to the nearest yard)?

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - $( 4 , - 4 )$

Answer the question. -In which quadrants do the square roots of i lie?

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle - 2,8 \rangle , \mathbf { v } = \langle - 9 , - 6 \rangle$ . Find $\mathbf { u } + \mathbf { v }$ .

Find the indicated angle or side. Give an exact answer. -Find the measure of angle A in degrees.

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - $( - 6,2 \sqrt { 3 } )$

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve. -

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

Determine whether the pair of vectors is orthogonal. - $\langle - 3 , \sqrt { 3 } \rangle , \langle - 2 \sqrt { 3 } , - 6 \rangle$

Give the rectangular coordinates for the point. - $\left( - 5,330 ^ { \circ } \right)$

Find the missing parts of the triangle. - =7 =30 =61 If necessary, round angles to the nearest degree and side lengths to the nearest yard.

Find the missing parts of the triangle. - =3 =5.95 =11.9 If necessary, round angles to the nearest degree and side lengths to the nearest hundredth.

Find all specified roots. -Eighth roots of $i$ .

Find all solutions of the equation. Leave answers in trigonometric form. - $\mathrm { x } ^ { 3 } + 8 = 0$

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

Review of Basic Concepts

Filters

Exam 8: Applications of Trigonometry

Give two parametric representations for the equation of the parabola. - y=(x+1)2−8y = ( x + 1 ) ^ { 2 } - 8y=(x+1)2−8

Find an equivalent equation in rectangular coordinates. - r=51+cos⁡θ\mathrm { r } = \frac { 5 } { 1 + \cos \theta }r=1+cosθ5​

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - 3(cos⁡315+isin⁡315)6(cos⁡45+isin⁡45)\frac { \sqrt { 3 } ( \cos 315 + i \sin 315 ) } { \sqrt { 6 } ( \cos 45 + i \sin 45 ) }6​(cos45+isin45)3​(cos315+isin315)​

Answer the question. -If n\mathrm { n }n is an even number, then which of the following statements is true?

Solve the problem. -Two points AAA and BBB are on opposite sides of a building. A surveyor chooses a third point C64C 64C64 yd from BBB and 93 yd from AAA , with angle ACBA C BACB measuring 67.3∘67.3 ^ { \circ }67.3∘ . How far apart are AAA and BBB (to the nearest yard)?

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - (4,−4)( 4 , - 4 )(4,−4)

Answer the question. -In which quadrants do the square roots of i lie?

Find the component form of the indicated vector. -Let u=⟨−2,8⟩,v=⟨−9,−6⟩\mathbf { u } = \langle - 2,8 \rangle , \mathbf { v } = \langle - 9 , - 6 \rangleu=⟨−2,8⟩,v=⟨−9,−6⟩ . Find u+v\mathbf { u } + \mathbf { v }u+v .

Find the indicated angle or side. Give an exact answer. -Find the measure of angle A in degrees.

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - (−6,23)( - 6,2 \sqrt { 3 } )(−6,23​)

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve. -

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

Determine whether the pair of vectors is orthogonal. - ⟨−3,3⟩,⟨−23,−6⟩\langle - 3 , \sqrt { 3 } \rangle , \langle - 2 \sqrt { 3 } , - 6 \rangle⟨−3,3​⟩,⟨−23​,−6⟩

Give the rectangular coordinates for the point. - (−5,330∘)\left( - 5,330 ^ { \circ } \right)(−5,330∘)

Find the missing parts of the triangle. - =7 =30 =61 If necessary, round angles to the nearest degree and side lengths to the nearest yard.

Find the missing parts of the triangle. - =3 =5.95 =11.9 If necessary, round angles to the nearest degree and side lengths to the nearest hundredth.

Find all specified roots. -Eighth roots of iii .

Find all solutions of the equation. Leave answers in trigonometric form. - x3+8=0\mathrm { x } ^ { 3 } + 8 = 0x3+8=0

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve. - x=2tan⁡t,y=5sec⁡tx = 2 \tan t , y = 5 \sec tx=2tant,y=5sect , for ttt in [0,2π][ 0,2 \pi ][0,2π]

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

Review of Basic Concepts

Filters

Give two parametric representations for the equation of the parabola. - $y = ( x + 1 ) ^ { 2 } - 8$

Find an equivalent equation in rectangular coordinates. - $\mathrm { r } = \frac { 5 } { 1 + \cos \theta }$

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { \sqrt { 3 } ( \cos 315 + i \sin 315 ) } { \sqrt { 6 } ( \cos 45 + i \sin 45 ) }$

Answer the question. -If $\mathrm { n }$ is an even number, then which of the following statements is true?

Solve the problem. -Two points $A$ and $B$ are on opposite sides of a building. A surveyor chooses a third point $C 64$ yd from $B$ and 93 yd from $A$ , with angle $A C B$ measuring $67.3 ^ { \circ }$ . How far apart are $A$ and $B$ (to the nearest yard)?

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - $( 4 , - 4 )$

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle - 2,8 \rangle , \mathbf { v } = \langle - 9 , - 6 \rangle$ . Find $\mathbf { u } + \mathbf { v }$ .

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - $( - 6,2 \sqrt { 3 } )$

Determine whether the pair of vectors is orthogonal. - $\langle - 3 , \sqrt { 3 } \rangle , \langle - 2 \sqrt { 3 } , - 6 \rangle$

Give the rectangular coordinates for the point. - $\left( - 5,330 ^ { \circ } \right)$

Find all specified roots. -Eighth roots of $i$ .

Find all solutions of the equation. Leave answers in trigonometric form. - $\mathrm { x } ^ { 3 } + 8 = 0$