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=(11\pi)/(2)-2\pi \\ \\ \theta=(11\pi)/(2)-(4\pi)/(2) \\ \\ \theta=(7\pi)/(2) \end{gathered}`

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

`\begin{gathered} \theta=(7\pi)/(2)-2\pi \\ \\ \theta=(7\pi)/(2)-(4\pi)/(2) \\ \\ \theta=(3\pi)/(2) \end{gathered}`

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

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

The answer is:

sin(theta) = -1

cos(theta) = 0