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Chapter 6: Q. 27 (page 437)

Write an equation for a sinusoidal graph with the following properties:

A =-3 period =2蟺3 phase shiftrole="math" localid="1646369214539" =-蟺4

Short Answer

Expert verified

The equation isy=-3sin3x+3蟺4.

Step by step solution

01

Step 1. Given Information

We are given A =-3period =2蟺3phase shift =-蟺4and we have to find the equation of the sinusoidal graph.

02

Step 2. Solve for ω 

If 蝇>0, the equation of the sinusoidal graph with amplitude A, period T=2蟺蝇and phase shift =鈭�蝇is y=Asin蝇x-鈭�.

We have, T=2蟺3

鈬�2蟺蝇=2蟺3鈬�蝇=3

03

Step 3. Solve for ∅

Substituting the value of 蝇=3in the equation of phase shift.

We get,

鈭�蝇=-蟺4鈬�鈭�3=-蟺4鈬�鈭�=-蟺4脳3鈬�鈭�=-3蟺4

04

Step 4. Finding the equation

Substituting all the values in the equation of the graph we get,

y=Asin(蝇x-鈭�)鈬�y=-3sin3x--3蟺4鈬�y=-3sin3x+3蟺4

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Most popular questions from this chapter

Nautical Miles A nautical mile equals the length of arc subtended by a central angle of 1 minute on a great circle鈥� on the surface of Earth. See the figure. If the radius of Earth is taken as 3960 miles, express 1 nautical mile in terms of ordinary, or statute, miles.

A __________ __________ is a positive angle whose vertex is at the center of a circle.

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

17掳

Covert each angle in degrees to radians. Express your answer as a multiple of 蟺.

Use a calculator to find the approximate value of each expression rounded to two decimal places.

tan蟺10
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