Question

Write the function y=-sin x as a phase shift of y=sin x.

Analyzing functions
ANSWERED
asked 2020-12-21
Write the function \(\displaystyle{y}=-{\sin{{x}}}\) as a phase shift of \(\displaystyle{y}={\sin{{x}}}\).

Answers (1)

2020-12-22
For a function \(\displaystyle{y}={\sin{{\left({x}+{a}\right)}}}\), a is a phase shift.
So \(\displaystyle{y}=-{\sin{{x}}}\)
\(\displaystyle{y}={\sin{{\left({x}+\pi\right)}}}\)
As the sine function is negative at \(\displaystyle{180}+θ\), the phase shift is \(\displaystyle\pi\)
\(\displaystyle{y}={\sin{{\left({x}+\pi\right)}}}\)
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