Question

question
given the following unit circle, rotate green dot to the appropriate angle and then find the exact value of the function.
\cos 315^{\circ}

Explanation:

Step1: Determine the reference angle

The angle $315^\circ$ is in the fourth quadrant. To find the reference angle, we use the formula for angles in the fourth quadrant: reference angle $= 360^\circ - \theta$. So, reference angle $= 360^\circ - 315^\circ = 45^\circ$.

Step2: Recall the cosine value of the reference angle

We know that $\cos 45^\circ = \frac{\sqrt{2}}{2}$.

Step3: Determine the sign of the cosine in the fourth quadrant

In the fourth quadrant, the cosine function is positive (since the x - coordinate, which corresponds to cosine on the unit circle, is positive in the fourth quadrant). So, $\cos 315^\circ=\cos(360^\circ - 45^\circ)=\cos 45^\circ=\frac{\sqrt{2}}{2}$.

Answer:

$\frac{\sqrt{2}}{2}$