Is \(\displaystyle{\sin{{\left(\omega{t}+\pi\right)}}}=-{\sin{\omega}}{t}\) always true no matter what

Emmy Decker

Emmy Decker

Answered question

2022-04-16

Is sin(ωt+π)=sinωt always true no matter what ω is?
For example, it's true that sin(t+π)=sin(t). You flip one over the x-axis, and you get the other. But sin(2t+π)=sin(2t). Because sin(2t) has a period of π, so if you translate it by π, you are still gonna get sin(2t)

Answer & Explanation

Sabrina Campos

Sabrina Campos

Beginner2022-04-17Added 13 answers

You are wrong: let u=2t; then
sin(2t+π)=sin(u+π)=sin(u)=sin(2t)
You are right when you assert that sin(2t+π) is periodic with period π, but what you extract from that is that
sin(2(tπ)+π)=2sin(2t+π)
in other words,
sin(2tπ)=sin(2t+π)

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