Find the exact values of (a) sin s, (b) cos s, and (c) tan s f...

Question

Find the exact values of (a) sin s, (b) cos s, and (c) tan s for each real number s. See Example 1.

s = ―π

Accepted Answer

Welcome back. I am so glad you're here. We are asked to determine the exact values of the sine of P. The cosine of P in the tangent of P where P is equal to negative seven pi. Our answer choices are answer choice. A sine of negative seven pi equals zero, cosine of negative seven pi equals one and tangent of negative seven pi equals zero. Answer choice B the sine of negative seven pi equals one. The cosine of negative seven pi equals zero. And the tangent of negative seven pi is undefined answer choice C the sine of negative seven pi equals zero. The cosine of negative seven pi equals negative one and the tangent of negative seven pi equals zero. And answer choice D the sine of negative seven pi equals negative one. The cosine of negative seven pi equals zero. And the tangent of negative seven pi is undefined. All right. So we're looking at this angle of negative seven pi but it's a little bit easier if our angle P is in between zero and two pie. So let's find a co terminal angle with negative seven pi between zero and two pi and we'll do that because negative seven pi is negative, we'll do that by adding two pi. So negative seven pi plus two pi is negative five pi not there yet add another two pi negative five pi plus two. Pi is negative three pi not there yet add another two pi negative three pi plus two pi is negative one pi not there yet. We'll add another pi another two pi excuse me, negative pi plus two pi is positive one pi and that is in between zero and two pi. We recall from previous lessons that pi is a quadrant angle. So taking a quick look at a very very brief sketch of a unit circle, definitely check out the figure of the unit circle in your textbook. For a more detailed version, we've got a vertical Y axis and horizontal X axis. They come together the origin in the middle. This is overlain with the unit circle. All the points on the unit circle are one unit away from the origin. That is not true of my drawing, but you can use your imagination. Now for pi it's got its initial side along the positive part of the X axis and its terminal side, we had counterclockwise all the way to the negative part of the X axis. Pi is 180 degrees. So that is right where the unit circle intercepts the negative part of the X axis. So the X and Y values here are negative 10. Why is that important? Well, because we recall from previous lessons that when we're finding the sign of an angle on the unit circle, that's going to be equal to Y when we're finding the cosine of an angle on the unit circle that's equal to X. And when we're finding the tangent of an angle on the unit circle, that's Y divided by X. So here Y is equal to zero, the sine of our angle P negative seven pi equals zero. Now cosine of P is equal to XX. Here is negative one. So the cosine of negative seven pi is negative one and it'll take a second longer. For the tangent. We have Y in the numerator that is zero divided by X in the denominator negative 10 divided by negative one is zero. So the tangent of our angle P which is negative seven pi is equal to zero. We look at our answer choices for zero, negative 10 and that matches with answer choice. C well done. We'll catch you on the next one.

Find the exact values of (a) sin s, (b) cos s, and (c) tan s for each real number s. See Example 1.
s = ―π

Key Concepts

Unit Circle

Trigonometric Functions

Angle Measurement

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