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Chapter 6: Q 13. (page 409)

Determine the amplitude and period of each function without graphing.
$y = - 4 \cos (2 x)$ .

Short Answer

Expert verified

Amplitude is 4 and period is $π$ .

Step by step solution

Step 1. Given Information.

Determine the amplitude and period of each function without graphing.

$y = - 4 \cos (2 x)$ .

Step 2. Evaluation.

For $ω > 0$ , the amplitude and period of $y = A \sin (ω x)$ are given by

Amplitude $= |A|$ and period $= T = \frac{2 π}{ω}$ .

On comapring, we get

$A = |- 4| = 4$

$ω = 2$

$T = \frac{2 π}{2} = π$ .

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Most popular questions from this chapter

In problems 13-20, $P (x, y)$ is the point on the unit circle that corresponds to a real number $t$ . Find the exact values of the six trigonometric functions of $t$ .

$(\frac{2 \sqrt{2}}{3}, - \frac{1}{3})$ .

In Example 6, we found that the distance between Albuquerque, New Mexico, and Glasgow, Montana, is approximately 903 miles. According to mapquest.com, the distance is approximately 1300 miles. What might account for the difference?

Write the equation of a sine function that has the given characteristics.

Amplitude: $3$

Period: $π$

In Problems 13–20, $P = (x, y)$ is the point on the unit circle that corresponds to a real number $t$ . Find the exact values of the six trigonometric functions of $t$ .

$(\frac{\sqrt{3}}{2}, \frac{1}{2})$ .

Convert each angle in degrees to radians. Express your answer in decimal form, round to two decimal places.

$17 °$

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Determine the amplitude and period of each function without graphing.y=-4cos2x.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Evaluation.

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Most popular questions from this chapter

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Determine the amplitude and period of each function without graphing.
$y = - 4 \cos (2 x)$ .