Exam 5: Trigonometric Functions

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - $\theta = \frac { \pi } { 4 }$ radians, $\mathrm { A } = 50$ square meters, $\mathrm { r } =$ ?

(Multiple Choice)

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Question 341

Find the exact value. Do not use a calculator. - $\sec \frac { \pi } { 3 }$

(Multiple Choice)

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Question 342

Find an equation for the graph. -

(Multiple Choice)

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Question 343

Find the exact value of the expression. Do not use a calculator. - $\sin 330 ^ { \circ } \sin 270 ^ { \circ }$

(Multiple Choice)

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Question 344

Without graphing the function, determine its amplitude or period as requested. - $y = \sin 3 x \quad$ Find the period.

(Multiple Choice)

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Question 345

Solve the problem. -A car is traveling at $50 \mathrm { mph }$ . If its tires have a diameter of 26 inches, how fast are the car's tires turning? Express the answer in revolutions per minute. If necessary, round to two decimal places.

(Multiple Choice)

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Question 346

Find an equation for the graph. -

(Multiple Choice)

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Question 347

Convert the angle in radians to degrees. - $- \frac { 7 \pi } { 10 }$

(Multiple Choice)

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Question 348

Find the exact value. Do not use a calculator. - $\cot 570 ^ { \circ }$

(Multiple Choice)

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Question 349

Answer the question. -Which one of the equations below matches the graph?

(Multiple Choice)

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Question 350

Write the word or phrase that best completes each statement or answers the question. -The following data represents the average monthly minimum temperature for a certain city in California. Month, x Average Monthly Minimum Temperature, January, 1 49.6 February, 2 50.8 March, 3 55.6 April, 4 57.5 May, 5 60.7 June, 6 63.6 July, 7 65.9 August, 8 65.6 September, 9 64.4 October, 10 62.1 November, 11 54.2 December, 12 50.1 Draw a scatter diagram of the data for one period. Find a sinusoidal function of the form y = A sin (ωx - Φ) + B that fits the data. Draw the sinusoidal function on the scatter diagram. Use a graphing utility to find the sinusoidal function of best fit. Draw the sinusoidal function of best fit on the scatter diagram. $Write the word or phrase that best completes each statement or answers the question. -The following data represents the average monthly minimum temperature for a certain city in California. \begin{array}{l|c} \text { Month, x } & \begin{array}{c} \text { Average Monthly } \\ \text { Minimum } \\ \text { Temperature, } \end{array} \\ \hline \text { January, } 1 & 49.6 \\ \text { February, } 2 & 50.8 \\ \text { March, } 3 & 55.6 \\ \text { April, } 4 & 57.5 \\ \text { May, } 5 & 60.7 \\ \text { June, } 6 & 63.6 \\ \text { July, } 7 & 65.9 \\ \text { August, } 8 & 65.6 \\ \text { September, } 9 & 64.4 \\ \text { October, } 10 & 62.1 \\ \text { November, 11 } & 54.2 \\ \text { December, 12 } & 50.1 \end{array} Draw a scatter diagram of the data for one period. Find a sinusoidal function of the form y = A sin (ωx - Φ) + B that fits the data. Draw the sinusoidal function on the scatter diagram. Use a graphing utility to find the sinusoidal function of best fit. Draw the sinusoidal function of best fit on the scatter diagram.$

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Question 351

Graph the function. - $y = 3 \sec \left( \frac { 1 } { 4 } x \right)$ $Graph the function. - y = 3 \sec \left( \frac { 1 } { 4 } x \right)$

(Multiple Choice)

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Question 352

Solve the problem. -A wheel of radius $3.4$ feet is moving forward at 18 feet per second. How fast is the wheel rotating?

(Multiple Choice)

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Question 353

Solve the problem. -If $f ( \theta ) = \sin \theta$ and $f ( a ) = - \frac { 1 } { 6 }$ , find the exact value of $f ( a ) + f ( a + 2 \pi ) + f ( a + 4 \pi )$ .

(Multiple Choice)

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Question 354

Showing 341 - 354 of 354

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - $\theta = \frac { \pi } { 4 }$ radians, $\mathrm { A } = 50$ square meters, $\mathrm { r } =$ ?

Find the exact value. Do not use a calculator. - $\sec \frac { \pi } { 3 }$

Find an equation for the graph. -

Find the exact value of the expression. Do not use a calculator. - $\sin 330 ^ { \circ } \sin 270 ^ { \circ }$

Without graphing the function, determine its amplitude or period as requested. - $y = \sin 3 x \quad$ Find the period.

Solve the problem. -A car is traveling at $50 \mathrm { mph }$ . If its tires have a diameter of 26 inches, how fast are the car's tires turning? Express the answer in revolutions per minute. If necessary, round to two decimal places.

Find an equation for the graph. -

Convert the angle in radians to degrees. - $- \frac { 7 \pi } { 10 }$

Find the exact value. Do not use a calculator. - $\cot 570 ^ { \circ }$

Answer the question. -Which one of the equations below matches the graph?

Graph the function. - $y = 3 \sec \left( \frac { 1 } { 4 } x \right)$ $Graph the function. - y = 3 \sec \left( \frac { 1 } { 4 } x \right)$

Solve the problem. -A wheel of radius $3.4$ feet is moving forward at 18 feet per second. How fast is the wheel rotating?

Solve the problem. -If $f ( \theta ) = \sin \theta$ and $f ( a ) = - \frac { 1 } { 6 }$ , find the exact value of $f ( a ) + f ( a + 2 \pi ) + f ( a + 4 \pi )$ .

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 5: Trigonometric Functions

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - θ=π4\theta = \frac { \pi } { 4 }θ=4π​ radians, A=50\mathrm { A } = 50A=50 square meters, r=\mathrm { r } =r= ?

Find the exact value. Do not use a calculator. - sec⁡π3\sec \frac { \pi } { 3 }sec3π​

Find an equation for the graph. -

Find the exact value of the expression. Do not use a calculator. - sin⁡330∘sin⁡270∘\sin 330 ^ { \circ } \sin 270 ^ { \circ }sin330∘sin270∘

Without graphing the function, determine its amplitude or period as requested. - y=sin⁡3xy = \sin 3 x \quady=sin3x Find the period.

Solve the problem. -A car is traveling at 50mph50 \mathrm { mph }50mph . If its tires have a diameter of 26 inches, how fast are the car's tires turning? Express the answer in revolutions per minute. If necessary, round to two decimal places.

Find an equation for the graph. -

Convert the angle in radians to degrees. - −7π10- \frac { 7 \pi } { 10 }−107π​

Find the exact value. Do not use a calculator. - cot⁡570∘\cot 570 ^ { \circ }cot570∘

Answer the question. -Which one of the equations below matches the graph?

Graph the function. - y=3sec⁡(14x)y = 3 \sec \left( \frac { 1 } { 4 } x \right)y=3sec(41​x)

Solve the problem. -A wheel of radius 3.43.43.4 feet is moving forward at 18 feet per second. How fast is the wheel rotating?

Solve the problem. -If f(θ)=sin⁡θf ( \theta ) = \sin \thetaf(θ)=sinθ and f(a)=−16f ( a ) = - \frac { 1 } { 6 }f(a)=−61​ , find the exact value of f(a)+f(a+2π)+f(a+4π)f ( a ) + f ( a + 2 \pi ) + f ( a + 4 \pi )f(a)+f(a+2π)+f(a+4π) .

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - $\theta = \frac { \pi } { 4 }$ radians, $\mathrm { A } = 50$ square meters, $\mathrm { r } =$ ?

Find the exact value. Do not use a calculator. - $\sec \frac { \pi } { 3 }$

Find the exact value of the expression. Do not use a calculator. - $\sin 330 ^ { \circ } \sin 270 ^ { \circ }$

Without graphing the function, determine its amplitude or period as requested. - $y = \sin 3 x \quad$ Find the period.

Solve the problem. -A car is traveling at $50 \mathrm { mph }$ . If its tires have a diameter of 26 inches, how fast are the car's tires turning? Express the answer in revolutions per minute. If necessary, round to two decimal places.

Convert the angle in radians to degrees. - $- \frac { 7 \pi } { 10 }$

Find the exact value. Do not use a calculator. - $\cot 570 ^ { \circ }$

Graph the function. - $y = 3 \sec \left( \frac { 1 } { 4 } x \right)$ $Graph the function. - y = 3 \sec \left( \frac { 1 } { 4 } x \right)$

Solve the problem. -A wheel of radius $3.4$ feet is moving forward at 18 feet per second. How fast is the wheel rotating?

Solve the problem. -If $f ( \theta ) = \sin \theta$ and $f ( a ) = - \frac { 1 } { 6 }$ , find the exact value of $f ( a ) + f ( a + 2 \pi ) + f ( a + 4 \pi )$ .