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Chapter 6: Q. 16 (page 429)

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

Amplitude:3

Period:蟺

Phase shift:2

Short Answer

Expert verified

The obtained equation from the given information is y=3sin2x-4

Step by step solution

01

Step 1.  Find the value of ω and ϕ 

We know that, T=2蟺蝇

So,

Substituting T=蟺2in the above equation, we get:

T=2蟺蝇蟺2=2蟺蝇蝇=4

We have:

蠒蝇=2蠒4=2蝇=4蠒=8

02

Step 2. Writing the equation 

The general sine equation is y=Asin蝇x-蠒.

Substituting A=3蝇=4蠒=8in the above equation, we get:

y=3sin4x-8y=3sin4x-2

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