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Chapter 6: Q. 18 (page 429)

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

Amplitude:2

Period:蟺

Phase shift:-2

Short Answer

Expert verified

The obtained equation from the given information isy=2sin2x+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in the above equation, we get:

T=2蟺蝇蟺=2蟺蝇蝇=2

We have:

蠒蝇=-2蠒2=-2蠒=-4

02

Step 2. Find the equation  

The genral sine function isy=Asin蝇x-蠒.

Substituting the value 蝇=2蠒=-4A=2in the general sine function, we get:

role="math" localid="1646391977430" y=2sin2x-(-4)y=2sin2x+4

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Most popular questions from this chapter

The range of the sine function is _____.

graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

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sin蟺8

In problems 13-20, Px,yis the point on the unit circle that corresponds to a real number t. Find the exact values of the six trigonometric functions of t.

-15,265.

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

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