Question

question
given the following unit circle, rotate green dot to the appropriate angle and then find the exact value of the function.
$cos 315^circ$
unit circle diagram with green dot on positive x - axis
answer
attempt 1 out of 2
$cos 315^circ = square$
submit answer
undefined $sqrt{quad}$

Explanation:

Step1: Determine the reference angle

The angle \(315^\circ\) is in the fourth quadrant. The reference angle is \(360^\circ - 315^\circ = 45^\circ\).

Step2: Recall the cosine value for the reference angle

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

Step3: Determine the sign of cosine in the fourth quadrant

In the fourth quadrant, cosine is positive. So, \(\cos 315^\circ=\cos(360^\circ - 45^\circ)=\cos 45^\circ=\frac{\sqrt{2}}{2}\).

Answer:

\(\frac{\sqrt{2}}{2}\)