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Chapter 6: Q 12. (page 409)

Determine the amplitude and period of each function without graphing.
$y = 3 \cos x$ .

Short Answer

Expert verified

The amplitude is 3 and period is $T = 2 π$ .

Step by step solution

01

Step 1. Given Information.

Determine the amplitude and period of each function without graphing.

$y = 3 \cos x$ .

02

Step 2. Evaluation.

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

amplitude $= |A|$ , Period $= \frac{2 π}{ω}$ .

On comparing, we get

Amplitude $|A| = 3$ .

Then, $ω = 1$

Period $= T = \frac{2 π}{1} = 2 π$ .

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Most popular questions from this chapter

Convert each angle in degrees to radians. Express your answer as a multiple of $π$ .

$- 180 °$

In the problem, $s$ denotes the length of the arc of a circle of radius $r$ subtended by the central angle $θ$ . Find the missing quantity. Round answers to three decimal places.

$θ = \frac{1}{3}$ radian, $s = 2$ feet , $r = ?$

An angle $θ$ is in ________ _________ if its vertex is at the origin of a rectangular coordinate system and its initial side coincides with the positive x-axis.

Use a calculator to find the approximate value of each expression rounded to two decimal places: $\csc \frac{5 π}{13}$

In Problems $4 - 6$ convert each angle in radians to degrees.

localid="1646375027881" $4 . - \frac{π}{8}$

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