Find each exact function value. See Example 2.
tan 3π/4

Question

Find each exact function value. See Example 2.

tan 3π/4

Accepted Answer

Welcome back. I am so glad you're here. We're asked to determine the exact value of the given function. Our given function is the tangent of seven pi divided by four. Our answer choices are answer choice, a one answer, choice B square root two, answer choice C negative square root two and answer choice D negative one. Well, we recall from previous lessons that the angle seven pi divided by four is an angle on the unit circle. So I am going to draw some of the unit circle but not the whole thing. Definitely be sure to reference the unit circle in your textbook for this. So we have a vertical y axis and a horizontal X axis. They come together at the origin in the middle, the unit circle lies over that and every point on the unit circle is one unit away from the origin. So you can use your imagination that what I drew is one unit away from the origin and a perfect circle. And for our angle seven pi divided by four, if we begin at the initial side along the positive part of the x axis and head counterclockwise seven pi divided by four is all the way in the fourth quadrant down into the right of the origin. So in radiance seven pi divided by four is equal to in degrees 315 degrees. And then you can also see from that diagram in your textbook that the X and Y coordinates at seven pi divided by four are square root two divided by two. That's the X coordinate and negative square root two divided by two. That's the Y coordinate. Now why is all this important? Well, we recall from previous lessons that when we have an angle on the unit circle, we'll call s when we take the tangent of that angle. S it is equal to Y divided by X. So our Y value is negative square root two divided by two. We'll divide that by our X value square root two divided by two. When we have fractions within fractions, I like to rewrite this with a division symbol. So negative square root two divided by two divided by square root two divided by two, which helps me remember to multiply by the reciprocal of the second fraction. So negative square root two divided by two multiplied by two divided by square root two, the reciprocal of that second fraction. And now look at all this canceling out that happens the square root twos cancel out the twos cancel out they're all ones. So retaining that negative, this is equal to negative one, the tangent of seven pi divided by four is equal to negative one. We look at our answer choices and this matches with answer choice. D well done. We'll catch you on the next one.

Find each exact function value. See Example 2.
tan 3π/4

Key Concepts

Unit Circle

Tangent Function

Reference Angles

Watch next

Find each exact function value. See Example 2.tan 3π/4

Key Concepts

Unit Circle

Tangent Function

Reference Angles

Watch next

Find each exact function value. See Example 2.
tan 3π/4