Verify the identity \sin(A+\pi)=-\sin A

amolent3u

amolent3u

Answered question

2021-12-11

Verify the identity sin(A+π)=sinA

Answer & Explanation

mauricio0815sh

mauricio0815sh

Beginner2021-12-12Added 34 answers

Use the Sum formula for sin:
sin(a+b)=sinαcosβ+cosαsinβ
sin(A+π)=sinAcosπ+cosAsinπ=sinA
sin(A+π)=sinA
sirpsta3u

sirpsta3u

Beginner2021-12-13Added 42 answers

You can prove it using unit circle:
If we add π to some angle θ, sinθ=sin(θ+π), but since they are on opposite parts of the center O, they have an opposite sign:
sin(A+π)=sinA

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