Question

For the angle, θ, determine the values of sinθ and cosθ: θ = 11π/2

Answer 1

When the measure of an angle exceeds 2pi we will subtract 2pi from it to make it less than 2pi

Since the given angle is 11/2 pi, then we will subtract 2pi from it to make it less than 2pi

$\begin{gathered} \theta=\frac{11\pi}{2}-2\pi \\ \\ \theta=\frac{11\pi}{2}-\frac{4\pi}{2} \\ \\ \theta=\frac{7\pi}{2} \end{gathered}$

It is still greater than 2 pi, then we will subtract another 2pi

$\begin{gathered} \theta=\frac{7\pi}{2}-2\pi \\ \\ \theta=\frac{7\pi}{2}-\frac{4\pi}{2} \\ \\ \theta=\frac{3\pi}{2} \end{gathered}$

Now, it is less than 2pi, then we will find its sine and cosine

$\begin{gathered} sin(\frac{3\pi}{2})=-1 \\ \\ cos(\frac{3\pi}{2})=0 \end{gathered}$

The answer is:

sin(theta) = -1

cos(theta) = 0