Find each exact function value. See Example 2.
cos 7π/4

Question

Find each exact function value. See Example 2.

cos 7π/4

Accepted Answer

Welcome back. I am so glad you're here. We are asked to determine the exact value of the given function. Our given function is the cosine of five pi divided by four. Our answer choices are answer choice, a negative square root two divided by two answer choice B one answer trace C negative square root three divided by two and answer trace D square root two divided by two. All right. So taking a look at our angle here, five pi divided by four, we can recognize from previous lessons and from the image of the unit circle in the textbook that five pi divided by four is an angle on the unit circle. So I'm going to draw a rough sketch of the unit circle. Definitely check out that image in the textbook for the details of the unit circle. We've got a vertical y axis and a horizontal X axis. They come together at the origin in the middle. Now, every point of the unit circle is one unit away from the origin. And you can imagine that what I'm drawing has every point on this circle, one unit away from the origin for five pi divided by four, we begin at the initial side along the positive part of the X axis. We had counterclockwise and five pi divided by four is going to be in quadrant three midway between the negative part of the X axis. And the, the negative part of the Y axis. There's our five pi divided by four that's in radiance and looking at those images in the textbook of the unit circle, that's the same as 225 degrees. And the X and Y coordinates for five pi divided by four are for X coordinate. It's negative square root two divided by two and the Y coordinate is also negative square root two divided by two. Now, why is this important? Well, we recall from previous lessons that the cosine of any angle along the unit circle. So here, the cosine of five pi divided by four is going to be equal to our X value. And the X value here is negative square root two divided by two. So negative square root two divided by two is our exact value. We look at our answer choices and that matches with answer choice. A well done. We'll catch you on the next one.

Find each exact function value. See Example 2.
cos 7π/4

Key Concepts

Unit Circle

Reference Angles

Trigonometric Values in Quadrants

Watch next

Find each exact function value. See Example 2.cos 7π/4

Key Concepts

Unit Circle

Reference Angles

Trigonometric Values in Quadrants

Watch next

Find each exact function value. See Example 2.
cos 7π/4