Question

The figure shown as an angle θ in standard position with its terminal side interesting the unit circle. Evaluate the indicated circular function value of θ.

Answer 1

Looking at the image, since the point (-5/13, 12/13) is on a unit circle, that means the x-coordinate is the cosine of angle theta and the y-coordinate is the sine of angle theta.

Since the point is in quadrant II, that means angle theta is between pi/2 and pi (in degrees: 90° and 180°).

Calculating the arc cosine of -5/13, we have:

`\begin{gathered} \cos (\theta)=-(5)/(13) \\ \theta=\cos ^(-1)(-(5)/(13)) \\ \theta=112.62\degree \end{gathered}`

Therefore the value of theta is 112.62°.