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/2

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 tangents of P where P is equal to three pi divided by two. Our answer choices are answer choice. A the sine of three pi divided by two equals negative one. The cosine of three pi divided by two equals zero. And the tangent of three pi divided by two is undefined answer choice B the sine of three pi divided by two equals zero. The cosine of three pi divided by two equals negative one. And the tangent of three pi divided by two equals zero. Answer choice C the sine of three pi divided by two equals one. The cosine of three pi divided by two equals zero. And the tangent of three pi divided by two is undefined and answer choice. D the sine of three pi divided by two equals negative one. The cosine of three pi divided by two equals zero. And the tangent of three pi divided by two equals zero. All right. So we're talking about the angle three pi divided by two. And we recall from previous lessons. And from the image of the unit circle in the textbook that three pi divided by two is a quadrant angle. Let's draw a quick sketch 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. The unit circle overlies that every point on the unit circle is exactly one unit away from the origin. That's not true of what I drew. But you can imagine that it is. And then for our angle of three pi divided by two, we begin with the initial side along the positive part of the X axis, we head counterclockwise and we're going to head all the way down to 270 degrees. This is the negative part of the Y axis. That's our three pi divided by two. And so from those images on the textbook and just knowing that every point on the unit circle is exactly one unit away from the origin, we know that the X coordinate here is zero and the Y coordinate here is negative one. Now, why is that important? Well, we recall from previous lessons that when we're talking about the unit circle, the sign of an angle is equal to the Y value, the cosine of our angle is equal to the X value and the tangent of an angle is equal to Y divided by X. So again, Y is negative one. So the sign of P equals negative one, the X value is zero. So the cosine of P equals zero. And for the tangent we have Y in the numerator that's negative one divided by X in the denominator, that's zero. Well, anything divided by zero is undefined. So the tangent of P, when P is three pi divided by two is undefined. We look at our answer choices for negative 10 and undefined and that matches with answer choice. A 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/2

Key Concepts

Unit Circle and Radian Measure

Definition of Sine, Cosine, and Tangent

Exact Values of Trigonometric Functions at Special Angles

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