38. -/2 points details my notes larpcalclimaga8 5.4.066. 0/6 submissions used write the expression as a…

38. -/2 points details my notes larpcalclimaga8 5.4.066. 0/6 submissions used write the expression as a trigonometric function of only θ, and use a graphing utility to confirm your answer graphically. sin(π + θ)

38. -/2 points details my notes larpcalclimaga8 5.4.066. 0/6 submissions used write the expression as a trigonometric function of only θ, and use a graphing utility to confirm your answer graphically. sin(π + θ)

Answer

Explanation:

Step1: Apply the sum - angle formula for sine

The sum - angle formula for sine is $\sin(A + B)=\sin A\cos B+\cos A\sin B$. Here $A = \pi$ and $B=\theta$. So, $\sin(\pi+\theta)=\sin\pi\cos\theta+\cos\pi\sin\theta$.

Step2: Evaluate $\sin\pi$ and $\cos\pi$

We know that $\sin\pi = 0$ and $\cos\pi=- 1$. Substituting these values into the above formula: $\sin\pi\cos\theta+\cos\pi\sin\theta=0\times\cos\theta+(-1)\times\sin\theta$.

Step3: Simplify the expression

$0\times\cos\theta+(-1)\times\sin\theta=-\sin\theta$.

Answer:

$-\sin\theta$