Exam 5: Trigonometric Functions

Match the given function to its graph. -1) $y = \sin \left( x - \frac { \pi } { 2 } \right)$ 2) $y = \cos \left( x + \frac { \pi } { 2 } \right)$ 3) $y = \sin \left( x + \frac { \pi } { 2 } \right)$ 4) $y = \cos \left( x - \frac { \pi } { 2 } \right)$ A. $Match the given function to its graph. -1) y = \sin \left( x - \frac { \pi } { 2 } \right) 2) y = \cos \left( x + \frac { \pi } { 2 } \right) 3) y = \sin \left( x + \frac { \pi } { 2 } \right) 4) y = \cos \left( x - \frac { \pi } { 2 } \right) A. B. C. D.$ B. $Match the given function to its graph. -1) y = \sin \left( x - \frac { \pi } { 2 } \right) 2) y = \cos \left( x + \frac { \pi } { 2 } \right) 3) y = \sin \left( x + \frac { \pi } { 2 } \right) 4) y = \cos \left( x - \frac { \pi } { 2 } \right) A. B. C. D.$ C. $Match the given function to its graph. -1) y = \sin \left( x - \frac { \pi } { 2 } \right) 2) y = \cos \left( x + \frac { \pi } { 2 } \right) 3) y = \sin \left( x + \frac { \pi } { 2 } \right) 4) y = \cos \left( x - \frac { \pi } { 2 } \right) A. B. C. D.$ D. $Match the given function to its graph. -1) y = \sin \left( x - \frac { \pi } { 2 } \right) 2) y = \cos \left( x + \frac { \pi } { 2 } \right) 3) y = \sin \left( x + \frac { \pi } { 2 } \right) 4) y = \cos \left( x - \frac { \pi } { 2 } \right) A. B. C. D.$

(Multiple Choice)

4.8/5

(77)

Question 181

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\sin \frac { 11 \pi } { 3 }$

(Multiple Choice)

4.9/5

(73)

Question 182

Without graphing the function, determine its amplitude or period as requested. - $y = - 4 \sin 5 x \quad$ Find the amplitude.

(Multiple Choice)

4.9/5

(95)

Question 183

Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - $y=\sin (\pi x)$ $Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - y=\sin (\pi x)$

(Multiple Choice)

4.8/5

(88)

Question 184

Use transformations to graph the function. - $y=3 \cos x+2$ $Use transformations to graph the function. - y=3 \cos x+2$

(Multiple Choice)

4.9/5

(79)

Question 185

In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. - $\left( \frac { 1 } { 5 } , - \frac { 2 \sqrt { 6 } } { 5 } \right) \quad$ Find $\csc t$

(Multiple Choice)

4.9/5

(79)

Question 186

Graph the function. - $y = - \sec x$ $Graph the function. - y = - \sec x$

(Multiple Choice)

4.9/5

(85)

Question 187

Convert the angle in degrees to radians. Express the answer in decimal form, rounded to two decimal places. - $- 308 ^ { \circ }$

(Multiple Choice)

4.9/5

(70)

Question 188

Choose the one alternative that best completes the statement or answers the question. In the problem, sin θ and cos θ are given. Find the exact value of the indicated trigonometric function. - $\sin \theta = \frac { 2 \sqrt { 2 } } { 3 } , \cos \theta = \frac { 1 } { 3 } \quad$ Find $\csc \theta$

(Multiple Choice)

4.8/5

(77)

Question 189

Write the word or phrase that best completes each statement or answers the question. -Salt Lake City, Utah, is due north of Flagstaff, Arizona. Find the distance between Salt Lake City (40°45' north latitude) and Flagstaff ( $35 ^ { \circ } 16 ^ { \prime }$ north latitude). Assume that the radius of the Earth is 3960 miles. Round to nearest whole mile.

(Short Answer)

5.0/5

(91)

Question 190

Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. - $\tan 50 ^ { \circ } - \frac { \sin 50 ^ { \circ } } { \cos 50 ^ { \circ } }$

(Multiple Choice)

4.9/5

(69)

Question 191

Find the exact value of the indicated trigonometric function of θ. - $\csc \theta = - \frac { 9 } { 4 } , \quad \theta$ in quadrant III $\quad$ Find $\cot \theta$

(Multiple Choice)

5.0/5

(76)

Question 192

Find the exact value of the indicated trigonometric function of θ. - $\tan \theta = - \frac { 8 } { 9 } , \quad \theta$ in quadrant II $\quad$ Find $\cos \theta$

(Multiple Choice)

4.8/5

(79)

Question 193

Find the exact value of the expression. Do not use a calculator. - $\cos \frac { \pi } { 3 } + \tan \frac { 5 \pi } { 3 }$

(Multiple Choice)

4.8/5

(82)

Question 194

Find the exact value of the expression if θ = 30°. Do not use a calculator. - $f ( \theta ) = \cos \theta \quad$ Find $11 f ( \theta )$ .

(Multiple Choice)

4.9/5

(73)

Question 195

Convert the angle to a decimal in degrees. Round the answer to two decimal places. - $59 ^ { \circ } 6 ^ { \prime } 24 "$

(Multiple Choice)

4.9/5

(77)

Question 196

Solve the problem. -If $\mathrm { f } ( \theta ) = \cos \theta$ and $\mathrm { f } ( \mathrm { a } ) = - \frac { 1 } { 4 }$ , find the exact value of $\mathrm { f } ( - \mathrm { a } )$

(Multiple Choice)

4.9/5

(71)

Question 197

Find the exact value of the expression. Do not use a calculator. - $\cos 120 ^ { \circ } \tan 60 ^ { \circ }$

(Multiple Choice)

4.8/5

(66)

Question 198

Find the exact value of the expression. Do not use a calculator. - $\sin \frac { \pi } { 3 } - \cos \frac { \pi } { 6 }$

(Multiple Choice)

4.7/5

(93)

Question 199

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. - $\mathrm { r } = 17$ inches, $\theta = 120 ^ { \circ } , \mathrm { A } =$ ?

(Multiple Choice)

4.8/5

(82)

Question 200

Showing 181 - 200 of 354

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\sin \frac { 11 \pi } { 3 }$

Without graphing the function, determine its amplitude or period as requested. - $y = - 4 \sin 5 x \quad$ Find the amplitude.

Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - $y=\sin (\pi x)$ $Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - y=\sin (\pi x)$

Use transformations to graph the function. - $y=3 \cos x+2$ $Use transformations to graph the function. - y=3 \cos x+2$

In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. - $\left( \frac { 1 } { 5 } , - \frac { 2 \sqrt { 6 } } { 5 } \right) \quad$ Find $\csc t$

Graph the function. - $y = - \sec x$ $Graph the function. - y = - \sec x$

Convert the angle in degrees to radians. Express the answer in decimal form, rounded to two decimal places. - $- 308 ^ { \circ }$

Choose the one alternative that best completes the statement or answers the question. In the problem, sin θ and cos θ are given. Find the exact value of the indicated trigonometric function. - $\sin \theta = \frac { 2 \sqrt { 2 } } { 3 } , \cos \theta = \frac { 1 } { 3 } \quad$ Find $\csc \theta$

Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. - $\tan 50 ^ { \circ } - \frac { \sin 50 ^ { \circ } } { \cos 50 ^ { \circ } }$

Find the exact value of the indicated trigonometric function of θ. - $\csc \theta = - \frac { 9 } { 4 } , \quad \theta$ in quadrant III $\quad$ Find $\cot \theta$

Find the exact value of the indicated trigonometric function of θ. - $\tan \theta = - \frac { 8 } { 9 } , \quad \theta$ in quadrant II $\quad$ Find $\cos \theta$

Find the exact value of the expression. Do not use a calculator. - $\cos \frac { \pi } { 3 } + \tan \frac { 5 \pi } { 3 }$

Find the exact value of the expression if θ = 30°. Do not use a calculator. - $f ( \theta ) = \cos \theta \quad$ Find $11 f ( \theta )$ .

Convert the angle to a decimal in degrees. Round the answer to two decimal places. - $59 ^ { \circ } 6 ^ { \prime } 24 "$

Solve the problem. -If $\mathrm { f } ( \theta ) = \cos \theta$ and $\mathrm { f } ( \mathrm { a } ) = - \frac { 1 } { 4 }$ , find the exact value of $\mathrm { f } ( - \mathrm { a } )$

Find the exact value of the expression. Do not use a calculator. - $\cos 120 ^ { \circ } \tan 60 ^ { \circ }$

Find the exact value of the expression. Do not use a calculator. - $\sin \frac { \pi } { 3 } - \cos \frac { \pi } { 6 }$

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. - $\mathrm { r } = 17$ inches, $\theta = 120 ^ { \circ } , \mathrm { A } =$ ?

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

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - sin⁡11π3\sin \frac { 11 \pi } { 3 }sin311π​

Without graphing the function, determine its amplitude or period as requested. - y=−4sin⁡5xy = - 4 \sin 5 x \quady=−4sin5x Find the amplitude.

Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - y=sin⁡(πx)y=\sin (\pi x)y=sin(πx)

Use transformations to graph the function. - y=3cos⁡x+2y=3 \cos x+2y=3cosx+2

Graph the function. - y=−sec⁡xy = - \sec xy=−secx

Convert the angle in degrees to radians. Express the answer in decimal form, rounded to two decimal places. - −308∘- 308 ^ { \circ }−308∘

Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. - tan⁡50∘−sin⁡50∘cos⁡50∘\tan 50 ^ { \circ } - \frac { \sin 50 ^ { \circ } } { \cos 50 ^ { \circ } }tan50∘−cos50∘sin50∘​

Find the exact value of the indicated trigonometric function of θ. - csc⁡θ=−94,θ\csc \theta = - \frac { 9 } { 4 } , \quad \thetacscθ=−49​,θ in quadrant III \quad Find cot⁡θ\cot \thetacotθ

Find the exact value of the indicated trigonometric function of θ. - tan⁡θ=−89,θ\tan \theta = - \frac { 8 } { 9 } , \quad \thetatanθ=−98​,θ in quadrant II \quad Find cos⁡θ\cos \thetacosθ

Find the exact value of the expression. Do not use a calculator. - cos⁡π3+tan⁡5π3\cos \frac { \pi } { 3 } + \tan \frac { 5 \pi } { 3 }cos3π​+tan35π​

Find the exact value of the expression if θ = 30°. Do not use a calculator. - f(θ)=cos⁡θf ( \theta ) = \cos \theta \quadf(θ)=cosθ Find 11f(θ)11 f ( \theta )11f(θ) .

Convert the angle to a decimal in degrees. Round the answer to two decimal places. - 59∘6′24"59 ^ { \circ } 6 ^ { \prime } 24 "59∘6′24"

Solve the problem. -If f(θ)=cos⁡θ\mathrm { f } ( \theta ) = \cos \thetaf(θ)=cosθ and f(a)=−14\mathrm { f } ( \mathrm { a } ) = - \frac { 1 } { 4 }f(a)=−41​ , find the exact value of f(−a)\mathrm { f } ( - \mathrm { a } )f(−a)

Find the exact value of the expression. Do not use a calculator. - cos⁡120∘tan⁡60∘\cos 120 ^ { \circ } \tan 60 ^ { \circ }cos120∘tan60∘

Find the exact value of the expression. Do not use a calculator. - sin⁡π3−cos⁡π6\sin \frac { \pi } { 3 } - \cos \frac { \pi } { 6 }sin3π​−cos6π​

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. - r=17\mathrm { r } = 17r=17 inches, θ=120∘,A=\theta = 120 ^ { \circ } , \mathrm { A } =θ=120∘,A= ?

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

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\sin \frac { 11 \pi } { 3 }$

Without graphing the function, determine its amplitude or period as requested. - $y = - 4 \sin 5 x \quad$ Find the amplitude.

Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - $y=\sin (\pi x)$ $Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - y=\sin (\pi x)$

Use transformations to graph the function. - $y=3 \cos x+2$ $Use transformations to graph the function. - y=3 \cos x+2$

Graph the function. - $y = - \sec x$ $Graph the function. - y = - \sec x$

Convert the angle in degrees to radians. Express the answer in decimal form, rounded to two decimal places. - $- 308 ^ { \circ }$

Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. - $\tan 50 ^ { \circ } - \frac { \sin 50 ^ { \circ } } { \cos 50 ^ { \circ } }$

Find the exact value of the indicated trigonometric function of θ. - $\csc \theta = - \frac { 9 } { 4 } , \quad \theta$ in quadrant III $\quad$ Find $\cot \theta$

Find the exact value of the indicated trigonometric function of θ. - $\tan \theta = - \frac { 8 } { 9 } , \quad \theta$ in quadrant II $\quad$ Find $\cos \theta$

Find the exact value of the expression. Do not use a calculator. - $\cos \frac { \pi } { 3 } + \tan \frac { 5 \pi } { 3 }$

Find the exact value of the expression if θ = 30°. Do not use a calculator. - $f ( \theta ) = \cos \theta \quad$ Find $11 f ( \theta )$ .

Convert the angle to a decimal in degrees. Round the answer to two decimal places. - $59 ^ { \circ } 6 ^ { \prime } 24 "$

Solve the problem. -If $\mathrm { f } ( \theta ) = \cos \theta$ and $\mathrm { f } ( \mathrm { a } ) = - \frac { 1 } { 4 }$ , find the exact value of $\mathrm { f } ( - \mathrm { a } )$

Find the exact value of the expression. Do not use a calculator. - $\cos 120 ^ { \circ } \tan 60 ^ { \circ }$

Find the exact value of the expression. Do not use a calculator. - $\sin \frac { \pi } { 3 } - \cos \frac { \pi } { 6 }$

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. - $\mathrm { r } = 17$ inches, $\theta = 120 ^ { \circ } , \mathrm { A } =$ ?