Question

1. if $sin \theta =.6000$, find the value of $sin(180^{circ}+\theta)$.

Explanation:

Step1: Use the trigonometric identity

The trigonometric identity for \(\sin(A + B)=\sin A\cos B+\cos A\sin B\). Here \(A = 180^{\circ}\) and \(B=\theta\). So \(\sin(180^{\circ}+\theta)=\sin180^{\circ}\cos\theta+\cos180^{\circ}\sin\theta\).
Since \(\sin180^{\circ}=0\) and \(\cos180^{\circ}=- 1\), the formula simplifies to \(\sin(180^{\circ}+\theta)=0\times\cos\theta+(-1)\times\sin\theta=-\sin\theta\).

Step2: Substitute the given value of \(\sin\theta\)

Given \(\sin\theta = 0.6000\). Substituting into the formula from Step1, we get \(\sin(180^{\circ}+\theta)=-0.6000\).

Answer:

\(-0.6000\)