establish the identity. cos(3π/2 - θ)= - sinθ choose the sequence of steps below that verifies the identity…

establish the identity. cos(3π/2 - θ)= - sinθ choose the sequence of steps below that verifies the identity. a. cos(3π/2 - θ)=cos 3π/2 cosθ - sin 3π/2 sinθ=(0)cosθ - (-1)sinθ= - sinθ b. cos(3π/2 - θ)=sin 3π/2 cosθ - cos 3π/2 sinθ=(0)cosθ+(0)sinθ= - sinθ c. cos(3π/2 - θ)=cos 3π/2 cosθ+sin 3π/2 sinθ=(0)cosθ+(-1)sinθ= - sinθ d. cos(3π/2 - θ)=sin 3π/2 cosθ+cos 3π/2 sinθ=(-1)cosθ - (0)sinθ= - sinθ

establish the identity. cos(3π/2 - θ)= - sinθ choose the sequence of steps below that verifies the identity. a. cos(3π/2 - θ)=cos 3π/2 cosθ - sin 3π/2 sinθ=(0)cosθ - (-1)sinθ= - sinθ b. cos(3π/2 - θ)=sin 3π/2 cosθ - cos 3π/2 sinθ=(0)cosθ+(0)sinθ= - sinθ c. cos(3π/2 - θ)=cos 3π/2 cosθ+sin 3π/2 sinθ=(0)cosθ+(-1)sinθ= - sinθ d. cos(3π/2 - θ)=sin 3π/2 cosθ+cos 3π/2 sinθ=(-1)cosθ - (0)sinθ= - sinθ

Answer

Explanation:

Step1: Recall the cosine - difference formula

The formula for $\cos(A - B)=\cos A\cos B+\sin A\sin B$. Here $A = \frac{3\pi}{2}$ and $B=\theta$. So $\cos(\frac{3\pi}{2}-\theta)=\cos\frac{3\pi}{2}\cos\theta+\sin\frac{3\pi}{2}\sin\theta$.

Step2: Evaluate trigonometric values

We know that $\cos\frac{3\pi}{2}=0$ and $\sin\frac{3\pi}{2}=- 1$. Substituting these values into the above - expression, we get $(0)\cos\theta+(-1)\sin\theta=-\sin\theta$.

Answer:

A. $\cos\left(\frac{3\pi}{2}-\theta\right)=\cos\frac{3\pi}{2}\cos\theta-\sin\frac{3\pi}{2}\sin\theta=(0)\cos\theta-(-1)\sin\theta = -\sin\theta$