if $\\sin\\theta = 0.6000$, find the value of $\\sin(180^{\\circ}+\\theta)$.
if $\\sin\\theta = 0.6000$, find the value of $\\sin(180^{\\circ}+\\theta)$.
Answer
Explanation:
Step1: Use the trigonometric identity
The trigonometric identity for (\sin(A + B)) is (\sin(A + B)=\sin A\cos B+\cos A\sin B). For (A = 180^{\circ}) and (B=\theta), we have (\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).
Step2: Substitute the value of (\sin\theta)
Given (\sin\theta = 0.6000), substituting into the simplified formula: (\sin(180^{\circ}+\theta)=-\sin\theta).
Answer:
(-0.6000)