6 multiple choice 1 point evaluate without using a calculator by using ratios in a reference triangle…

6 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}

6 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}

Answer

Explanation:

Step1: Use the property of cosine function

Since (\cos(-x)=\cos(x)), so (\cos(-\frac{5\pi}{4})=\cos(\frac{5\pi}{4})).

Step2: Find the reference angle

(\frac{5\pi}{4}=\pi+\frac{\pi}{4}). The reference angle (\theta'=\frac{5\pi}{4}-\pi=\frac{\pi}{4}).

Step3: Determine the sign

(\frac{5\pi}{4}) is in the third - quadrant. In the third - quadrant, (\cos(x)<0).

Step4: Use the cosine ratio 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})) (because of the sign in the third - quadrant).

Answer:

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