Question

question 3 of 10
evaluate \\(\cos 315^{\circ}\\) without using a calculator.
\\(\bigcirc\\) a. \\(-\frac{1}{2}\\)
\\(\bigcirc\\) b. \\(\frac{\sqrt{2}}{2}\\)
\\(\bigcirc\\) c. \\(\frac{\sqrt{3}}{2}\\)
\\(\bigcirc\\) d. \\(-\frac{\sqrt{2}}{2}\\)

Explanation:

Step1: Find the reference angle

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

Step2: Determine the sign of cosine

In the fourth quadrant, cosine is positive.

Step3: Evaluate cosine of the reference angle

We know that \( \cos 45^\circ = \frac{\sqrt{2}}{2} \). Since cosine is positive in the fourth quadrant, \( \cos 315^\circ = \cos 45^\circ = \frac{\sqrt{2}}{2} \).

Answer:

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