Question

structional video then use the problems to the right to practice and learn the concepts.
rcle to evaluate trig values in radian measure
.5 use the unit circle to e
8
multiple choice 1 point
evaluate without using a calculator by using ratios in a reference triangle.
cos(-\frac{5\pi}{4})
\frac{\sqrt{3}}{2}
-\frac{\sqrt{2}}{2}
-\frac{\sqrt{3}}{2}
\frac{1}{2}
9
multiple choice 1 point
evaluate without using a calculator by using ratios in a reference triangle.

Explanation:

Step1: Use the property of cosine function

The cosine function is even, so \(\cos(-x)=\cos(x)\). Then \(\cos(-\frac{5\pi}{4})=\cos(\frac{5\pi}{4})\).

Step2: Find the reference angle

For \(\theta=\frac{5\pi}{4}\), the reference angle \(\theta_{r}=\frac{5\pi}{4}-\pi=\frac{\pi}{4}\).

Step3: Determine the sign

The angle \(\frac{5\pi}{4}\) is in the third - quadrant. In the third - quadrant, the cosine function is negative.

Step4: Use the cosine of the reference angle

We know that \(\cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}\). So \(\cos(\frac{5\pi}{4})=-\cos(\frac{\pi}{4})\)

Answer:

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