Mathematics: Verify sin(360º - θ)= -sin θ show your work

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Verify sin(360º - θ)= -sin θ show your work

Tcareyoliver

14.03.2022

The verification is in the explanation.

Step-by-step explanation:

To solve this I'm going to use the difference identity for sine:

$\sin(a-b)=\sin(a)\cos(b)-\sin(b)\cos(a)$ .

$\sin(360^\circ-\theta)=\sin(360^\circ)\cos(\theta)-\sin(\theta)\cos(360^\circ)$

We are going to apply that $\sin(360^\circ)=0 \text{ while } \cos(360^\circ)=1$

$\sin(360^\circ-\theta)=0 \cdot \cos(\theta)-\sin(\theta)\cdot 1$

$\sin(360^\circ-\theta)=-\sin(\theta)$

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