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