Exam 6: The Circular Functions and Their Graphs

Graph the function over a one-period interval. - $y = 3 \cos \left( x + \frac { \pi } { 2 } \right)$ $Graph the function over a one-period interval. - y = 3 \cos \left( x + \frac { \pi } { 2 } \right)$

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Question 281

Graph the function over a one-period interval. - $y=1+\frac{1}{2} \cos 4\left(x+\frac{\pi}{2}\right)$ $Graph the function over a one-period interval. - y=1+\frac{1}{2} \cos 4\left(x+\frac{\pi}{2}\right)$

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Question 282

Solve the problem. -Suppose the tip of the minute hand of a clock is 9 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in 50 minutes. Give an exact answer.

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Question 283

Find the exact value of s in the given interval that has the given circular function value. - $\left[ \frac { 3 \pi } { 2 } , 2 \pi \right] ; \cos s = \frac { 1 } { 2 }$

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Question 284

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the distance between City E, $43 ^ { \circ } \mathrm { N }$ and City $\mathrm { F } , 64 ^ { \circ } \mathrm { S }$ . (Round to the nearest kilometer.)

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Question 285

Solve the problem. -A pulley with a diameter of 27 inches is driven by a belt which is moving $902 \mathrm { ft } / \mathrm { min }$ . To the nearest unit, how many revolutions per minute are made by the pulley?

(Multiple Choice)

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Question 286

Find the specified quantity. -Find the period of $y = - 5 \sin \left( 8 x + \frac { \pi } { 2 } \right)$ .

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Question 287

Graph the function. - $y=\frac{5}{3} \sec \left(\frac{3}{4} x+\frac{\pi}{3}\right)$ $Graph the function. - y=\frac{5}{3} \sec \left(\frac{3}{4} x+\frac{\pi}{3}\right)$

(Multiple Choice)

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Question 288

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the distance between City A, $28 ^ { \circ } \mathrm { N }$ and City B, $14 ^ { \circ } \mathrm { N }$ . (Round to the nearest kilometer.)

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Question 289

Showing 281 - 289 of 289

Graph the function over a one-period interval. - $y = 3 \cos \left( x + \frac { \pi } { 2 } \right)$ $Graph the function over a one-period interval. - y = 3 \cos \left( x + \frac { \pi } { 2 } \right)$

Graph the function over a one-period interval. - $y=1+\frac{1}{2} \cos 4\left(x+\frac{\pi}{2}\right)$ $Graph the function over a one-period interval. - y=1+\frac{1}{2} \cos 4\left(x+\frac{\pi}{2}\right)$

Solve the problem. -Suppose the tip of the minute hand of a clock is 9 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in 50 minutes. Give an exact answer.

Find the exact value of s in the given interval that has the given circular function value. - $\left[ \frac { 3 \pi } { 2 } , 2 \pi \right] ; \cos s = \frac { 1 } { 2 }$

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the distance between City E, $43 ^ { \circ } \mathrm { N }$ and City $\mathrm { F } , 64 ^ { \circ } \mathrm { S }$ . (Round to the nearest kilometer.)

Solve the problem. -A pulley with a diameter of 27 inches is driven by a belt which is moving $902 \mathrm { ft } / \mathrm { min }$ . To the nearest unit, how many revolutions per minute are made by the pulley?

Find the specified quantity. -Find the period of $y = - 5 \sin \left( 8 x + \frac { \pi } { 2 } \right)$ .

Graph the function. - $y=\frac{5}{3} \sec \left(\frac{3}{4} x+\frac{\pi}{3}\right)$ $Graph the function. - y=\frac{5}{3} \sec \left(\frac{3}{4} x+\frac{\pi}{3}\right)$

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the distance between City A, $28 ^ { \circ } \mathrm { N }$ and City B, $14 ^ { \circ } \mathrm { N }$ . (Round to the nearest kilometer.)

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

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Exam 6: The Circular Functions and Their Graphs

Graph the function over a one-period interval. - y=3cos⁡(x+π2)y = 3 \cos \left( x + \frac { \pi } { 2 } \right)y=3cos(x+2π​)

Graph the function over a one-period interval. - y=1+12cos⁡4(x+π2)y=1+\frac{1}{2} \cos 4\left(x+\frac{\pi}{2}\right)y=1+21​cos4(x+2π​)

Solve the problem. -Suppose the tip of the minute hand of a clock is 9 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in 50 minutes. Give an exact answer.

Find the exact value of s in the given interval that has the given circular function value. - [3π2,2π];cos⁡s=12\left[ \frac { 3 \pi } { 2 } , 2 \pi \right] ; \cos s = \frac { 1 } { 2 }[23π​,2π];coss=21​

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the distance between City E, 43∘N43 ^ { \circ } \mathrm { N }43∘N and City F,64∘S\mathrm { F } , 64 ^ { \circ } \mathrm { S }F,64∘S . (Round to the nearest kilometer.)

Solve the problem. -A pulley with a diameter of 27 inches is driven by a belt which is moving 902ft/min902 \mathrm { ft } / \mathrm { min }902ft/min . To the nearest unit, how many revolutions per minute are made by the pulley?

Find the specified quantity. -Find the period of y=−5sin⁡(8x+π2)y = - 5 \sin \left( 8 x + \frac { \pi } { 2 } \right)y=−5sin(8x+2π​) .

Graph the function. - y=53sec⁡(34x+π3)y=\frac{5}{3} \sec \left(\frac{3}{4} x+\frac{\pi}{3}\right)y=35​sec(43​x+3π​)

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the distance between City A, 28∘N28 ^ { \circ } \mathrm { N }28∘N and City B, 14∘N14 ^ { \circ } \mathrm { N }14∘N . (Round to the nearest kilometer.)

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Graph the function over a one-period interval. - $y = 3 \cos \left( x + \frac { \pi } { 2 } \right)$ $Graph the function over a one-period interval. - y = 3 \cos \left( x + \frac { \pi } { 2 } \right)$

Graph the function over a one-period interval. - $y=1+\frac{1}{2} \cos 4\left(x+\frac{\pi}{2}\right)$ $Graph the function over a one-period interval. - y=1+\frac{1}{2} \cos 4\left(x+\frac{\pi}{2}\right)$

Find the exact value of s in the given interval that has the given circular function value. - $\left[ \frac { 3 \pi } { 2 } , 2 \pi \right] ; \cos s = \frac { 1 } { 2 }$

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the distance between City E, $43 ^ { \circ } \mathrm { N }$ and City $\mathrm { F } , 64 ^ { \circ } \mathrm { S }$ . (Round to the nearest kilometer.)

Solve the problem. -A pulley with a diameter of 27 inches is driven by a belt which is moving $902 \mathrm { ft } / \mathrm { min }$ . To the nearest unit, how many revolutions per minute are made by the pulley?

Find the specified quantity. -Find the period of $y = - 5 \sin \left( 8 x + \frac { \pi } { 2 } \right)$ .

Graph the function. - $y=\frac{5}{3} \sec \left(\frac{3}{4} x+\frac{\pi}{3}\right)$ $Graph the function. - y=\frac{5}{3} \sec \left(\frac{3}{4} x+\frac{\pi}{3}\right)$

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the distance between City A, $28 ^ { \circ } \mathrm { N }$ and City B, $14 ^ { \circ } \mathrm { N }$ . (Round to the nearest kilometer.)