Find each exact function value.
sin ( ―5π/6)

Question

Find each exact function value.

sin ( ―5π/6)

Accepted Answer

Welcome back everyone. In this problem, we want to determine the exact value of the function of the sine of negative three pi divided by four. For our answer choices A is the negative of the square root of two divided by two B is the negative of the square root of three divided by two C is the square root of three divided by two and D is the square root of two divided by two. Now to help us find the exact value, it helps for us to think about the nature of the sine function. What do we know? Well, recall that the sine function is an odd function. And that what that means is that the sine of negative X, the sign of negative acts would be equal to the negative value of the sine of X. So how does that help us here? Well, we have a negative value that we're finding the sine of. So by applying that idea, then we can rewrite the sine of negative three pi divided by four as the negative value of the sine of three pi divided by four. So if we can find this value, then we can make it negative. Now, how are we going to find the sine of three pi divided by four? Well, let's put it on a unit circle. Now, on the unit circle, OK. On the unit circle, let's draw it over here to our right. And let's put our axes on our unit circle. So you know, we have our X axis and we have our Y axis. Then if we're putting the angle 3/4 of pi radiance, OK, then it would land somewhere right here. OK. So that's 3/4 of pie radiance. Now, what do we know? Well, we also know that each coordinate on the unit circle is written in the form of the cosine of theta for the X value and the sine of theta for the Y value. So if we're finding the sign of three quarters of pi, then that would have been our Y value. So let's represent it here. So let's imagine that we've come across on our unit circle. Well, notice that in our quadrant between zero and a half of pi there's also another X value as a matter of fact that X value, if I were to put it in blue here, that X value would actually be equivalent to 1/4 of pi. OK. So what does this mean? Then from our unit circle? This tells us that the sign, the sign of three quarters of pie, the value is actually equivalent to the s of a quarter of P, the sign of a quarter of pie. As a matter of fact, let me put that in blue just to distinguish them. OK? So that means then that if we know the value for the sign of a quarter of pie, we know what the sign of three quarters of pie is. But we do know that value, we know that that value equals the square root of two divided by two. So what does this tell us then? Well, that tells us that the sign of negative three pi divided by four then must be equal to the negative value of the square root of two divided by two. That would be the exact value for our expression. And when we look back on our answer choices, that would have been answer choice. A thanks a lot for watching everyone. I hope this video helped.

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Find each exact function value.sin ( ―5π/6)

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Defining the Unit Circle practice set

Find each exact function value.
sin ( ―5π/6)