Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. -\[\begin{array} { l } \mathrm { C } = 105 ^ { \circ } \\ \mathrm { a } = 6.7 \mathrm {~m} \\ \mathrm {~b} = 9.3 \mathrm {~m} \end{array}\]

A) $\mathrm { c } = 15.7 \mathrm {~m} , \mathrm {~A} = 32.4 ^ { \circ } , \mathrm { B } = 42.6 ^ { \circ }$ B) No triangle satisfies the given conditions. C) $\mathrm { c } = 18.6 \mathrm {~m} , \mathrm {~A} = 28.4 ^ { \circ } , \mathrm { B } = 46.6 ^ { \circ }$ D) $\mathrm { c } = 12.8 \mathrm {~m} , \mathrm {~A} = 30.4 ^ { \circ } , \mathrm { B } = 44.6 ^ { \circ }$ A) $\mathrm { c } = 15.7 \mathrm {~m} , \mathrm {~A} = 32.4 ^ { \circ } , \mathrm { B } = 42.6 ^ { \circ }$ B) No triangle satisfies the given conditions. C) $\mathrm { c } = 18.6 \mathrm {~m} , \mathrm {~A} = 28.4 ^ { \circ } , \mathrm { B } = 46.6 ^ { \circ }$ D) $\mathrm { c } = 12.8 \mathrm {~m} , \mathrm {~A} = 30.4 ^ { \circ } , \mathrm { B } = 44.6 ^ { \circ }$

Find the missing parts of the triangle. -\[\begin{array} { l } \mathrm { C } = 106 ^ { \circ } \\ \mathrm { c } = 44 \mathrm {~km} \\ \mathrm { a } = 54 \mathrm {~km} \end{array}\] If necessary, round angles to the nearest degree and side lengths to the nearest $\mathrm { km }$.

A) $A = 45 ^ { \circ } , B = 81 ^ { \circ } , b = 65 \mathrm {~km}$ B) no such triangle C) $A = 44 ^ { \circ } , B = 82 ^ { \circ } , b = 59 \mathrm {~km}$ D) $A = 44 ^ { \circ } , B = 82 ^ { \circ } , b = 62 \mathrm {~km}$ A) $A = 45 ^ { \circ } , B = 81 ^ { \circ } , b = 65 \mathrm {~km}$ B) no such triangle C) $A = 44 ^ { \circ } , B = 82 ^ { \circ } , b = 59 \mathrm {~km}$ D) $A = 44 ^ { \circ } , B = 82 ^ { \circ } , b = 62 \mathrm {~km}$

Exam 9: Applications of Trigonometry

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 8 ( \cos 90 + i \sin 90 ) } { 3 ( \cos 30 + i \sin 30 ) }$

(Multiple Choice)

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Question 221

Given that the polar equation r models the orbits of the planets about the sun, - $r = \frac { a \left( 1 - e ^ { 2 } \right) } { 1 + e \cos \theta }$ estimate the closest possible approach of a planet for which a = 14 and e = 0.4 to a planet for which a = 38 and e = 0.008.

(Multiple Choice)

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Question 222

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 a

(Multiple Choice)

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Question 223

Find an equivalent equation in rectangular coordinates. - $r - 5 \sin \theta = 6 \cos \theta$

(Multiple Choice)

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Question 224

Plot the point. - $\left( 2 , \frac { 9 \pi } { 4 } \right)$ $Plot the point. - \left( 2 , \frac { 9 \pi } { 4 } \right)$

(Multiple Choice)

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Question 225

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. - =10 =6.7 =9.3

(Multiple Choice)

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Question 226

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve. - $x = \sqrt { t } , y = 3 t + 4$ , for $t$ in $[ 0,4 ]$ $Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve. - x = \sqrt { t } , y = 3 t + 4 , for t in [ 0,4 ]$

(Multiple Choice)

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Question 227

The rectangular coordinates of a point are given. Express the point in polar coordinates with $r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$ - $( - \sqrt { 5 } , - \sqrt { 5 } )$

(Multiple Choice)

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Question 228

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 wind has an easterly component of $8 \mathrm {~km} / \mathrm { h }$ and a northerly component of $12 \mathrm {~km} / \mathrm { h }$ . Find the direction of the wind.

(Multiple Choice)

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Question 229

Draw a sketch to represent the vector. Refer to the vectors pictured here. -b + c

(Multiple Choice)

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Question 230

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. -Find the area of a triangular garden if the sides are approximately 6 feet, 11 feet, and 12 feet (to the nearest square foot).

(Multiple Choice)

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Question 231

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 4 } + 16 i = 0$

(Multiple Choice)

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Question 232

Find the missing parts of the triangle. - =10 =44 =54 If necessary, round angles to the nearest degree and side lengths to the nearest $\mathrm { km }$ .

(Multiple Choice)

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Question 233

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle - 6 , - 2 \rangle , \mathbf { v } = \langle - 7 , - 6 \rangle$ . Find $7 u - 5 \mathbf { v }$ .

(Multiple Choice)

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Question 234

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

(Multiple Choice)

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Question 235

Graph the polar equation for $\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$ - $r = 3 ( 1 + 3 \sin \theta )$ $Graph the polar equation for \theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right) - r = 3 ( 1 + 3 \sin \theta )$

(Multiple Choice)

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Question 236

Find the polar coordinates of the point(s) of intersection of the given curves for 0 $0 \leq \theta < 2 \pi$ - $r = 7 + 5 \sin \theta , r = 7 + 5 \cos \theta$

(Multiple Choice)

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Question 237

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $x = \sin t , y = \cos t ; t = \frac { \pi } { 6 }$

(Multiple Choice)

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Question 238

Answer the question. -What complex number is the common cube root of $- i$ and fourth root of 1 ?

(Multiple Choice)

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Question 239

The graph of a polar equation is given. Select the polar equation for the graph. -

(Multiple Choice)

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Question 240

Showing 221 - 240 of 447

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 8 ( \cos 90 + i \sin 90 ) } { 3 ( \cos 30 + i \sin 30 ) }$

Given that the polar equation r models the orbits of the planets about the sun, - $r = \frac { a \left( 1 - e ^ { 2 } \right) } { 1 + e \cos \theta }$ estimate the closest possible approach of a planet for which a = 14 and e = 0.4 to a planet for which a = 38 and e = 0.008.

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 a

Find an equivalent equation in rectangular coordinates. - $r - 5 \sin \theta = 6 \cos \theta$

Plot the point. - $\left( 2 , \frac { 9 \pi } { 4 } \right)$ $Plot the point. - \left( 2 , \frac { 9 \pi } { 4 } \right)$

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. - =10 =6.7 =9.3

The rectangular coordinates of a point are given. Express the point in polar coordinates with $r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$ - $( - \sqrt { 5 } , - \sqrt { 5 } )$

Draw a sketch to represent the vector. Refer to the vectors pictured here. -b + c

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. -Find the area of a triangular garden if the sides are approximately 6 feet, 11 feet, and 12 feet (to the nearest square foot).

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 4 } + 16 i = 0$

Find the missing parts of the triangle. - =10 =44 =54 If necessary, round angles to the nearest degree and side lengths to the nearest $\mathrm { km }$ .

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle - 6 , - 2 \rangle , \mathbf { v } = \langle - 7 , - 6 \rangle$ . Find $7 u - 5 \mathbf { v }$ .

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

Graph the polar equation for $\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$ - $r = 3 ( 1 + 3 \sin \theta )$ $Graph the polar equation for \theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right) - r = 3 ( 1 + 3 \sin \theta )$

Find the polar coordinates of the point(s) of intersection of the given curves for 0 $0 \leq \theta < 2 \pi$ - $r = 7 + 5 \sin \theta , r = 7 + 5 \cos \theta$

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $x = \sin t , y = \cos t ; t = \frac { \pi } { 6 }$

Answer the question. -What complex number is the common cube root of $- i$ and fourth root of 1 ?

The graph of a polar equation is given. Select the polar equation for the graph. -

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

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Exam 9: Applications of Trigonometry

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - 8(cos⁡90+isin⁡90)3(cos⁡30+isin⁡30)\frac { 8 ( \cos 90 + i \sin 90 ) } { 3 ( \cos 30 + i \sin 30 ) }3(cos30+isin30)8(cos90+isin90)​

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 a

Find an equivalent equation in rectangular coordinates. - r−5sin⁡θ=6cos⁡θr - 5 \sin \theta = 6 \cos \thetar−5sinθ=6cosθ

Plot the point. - (2,9π4)\left( 2 , \frac { 9 \pi } { 4 } \right)(2,49π​)

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. - =10 =6.7 =9.3

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve. - x=t,y=3t+4x = \sqrt { t } , y = 3 t + 4x=t​,y=3t+4 , for ttt in [0,4][ 0,4 ][0,4]

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∘. - (−5,−5)( - \sqrt { 5 } , - \sqrt { 5 } )(−5​,−5​)

Draw a sketch to represent the vector. Refer to the vectors pictured here. -b + c

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. -Find the area of a triangular garden if the sides are approximately 6 feet, 11 feet, and 12 feet (to the nearest square foot).

Find all solutions of the equation. Leave answers in trigonometric form. - x4+16i=0x ^ { 4 } + 16 i = 0x4+16i=0

Find the missing parts of the triangle. - =10 =44 =54 If necessary, round angles to the nearest degree and side lengths to the nearest km\mathrm { km }km .

Find the component form of the indicated vector. -Let u=⟨−6,−2⟩,v=⟨−7,−6⟩\mathbf { u } = \langle - 6 , - 2 \rangle , \mathbf { v } = \langle - 7 , - 6 \rangleu=⟨−6,−2⟩,v=⟨−7,−6⟩ . Find 7u−5v7 u - 5 \mathbf { v }7u−5v .

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

Graph the polar equation for θ in [0∘,360∘)\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)θ in [0∘,360∘) - r=3(1+3sin⁡θ)r = 3 ( 1 + 3 \sin \theta )r=3(1+3sinθ)

Find the polar coordinates of the point(s) of intersection of the given curves for 0 0≤θ<2π0 \leq \theta < 2 \pi0≤θ<2π - r=7+5sin⁡θ,r=7+5cos⁡θr = 7 + 5 \sin \theta , r = 7 + 5 \cos \thetar=7+5sinθ,r=7+5cosθ

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=π6x = \sin t , y = \cos t ; t = \frac { \pi } { 6 }x=sint,y=cost;t=6π​

Answer the question. -What complex number is the common cube root of −i- i−i and fourth root of 1 ?

The graph of a polar equation is given. Select the polar equation for the graph. -

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

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 8 ( \cos 90 + i \sin 90 ) } { 3 ( \cos 30 + i \sin 30 ) }$

Find an equivalent equation in rectangular coordinates. - $r - 5 \sin \theta = 6 \cos \theta$

Plot the point. - $\left( 2 , \frac { 9 \pi } { 4 } \right)$ $Plot the point. - \left( 2 , \frac { 9 \pi } { 4 } \right)$

The rectangular coordinates of a point are given. Express the point in polar coordinates with $r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$ - $( - \sqrt { 5 } , - \sqrt { 5 } )$

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 4 } + 16 i = 0$

Find the missing parts of the triangle. - =10 =44 =54 If necessary, round angles to the nearest degree and side lengths to the nearest $\mathrm { km }$ .

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle - 6 , - 2 \rangle , \mathbf { v } = \langle - 7 , - 6 \rangle$ . Find $7 u - 5 \mathbf { v }$ .

Graph the polar equation for $\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$ - $r = 3 ( 1 + 3 \sin \theta )$ $Graph the polar equation for \theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right) - r = 3 ( 1 + 3 \sin \theta )$

Find the polar coordinates of the point(s) of intersection of the given curves for 0 $0 \leq \theta < 2 \pi$ - $r = 7 + 5 \sin \theta , r = 7 + 5 \cos \theta$

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $x = \sin t , y = \cos t ; t = \frac { \pi } { 6 }$

Answer the question. -What complex number is the common cube root of $- i$ and fourth root of 1 ?