Find each exact function value. See Example 3.
sin π/3

Question

Find each exact function value. See Example 3.

sin π/3

Accepted Answer

Welcome back, everyone. In this problem, we want to determine the exact value of the sine of 1/6 of pi. For our answer choices A is a half, B is two, C is the square root of three and D is the square root of three divided by two. Now, if we're going to figure out the exact value of our function, it would be great to think about our function in a right triangle. So what do we know about the sign of 1/6 of pi radiance? Well, 1/6 of pi radiance is the same as 30 degrees. And that sixth of py radiance for is a part of what we call the special triangle. OK. So if I were to sketch it right here in our special triangle, what we know is that for this right triangle, if one of the shorter sides is one and the hypotenuse is two, then the other side must be equal to the square root of three. And in this right triangle, the side opposite to the side with one unit is 1/6 of pi while the side opposite to the side with the square root of three is a third of pi. OK. No, this triangle is very helpful because we can find the sine of a six stuff pie using what we know about the sine function. Because recall, eh recall that the sign of an angle equals the opposite side or is the ratio of the opposite side to the hypotenuse. Now, if we look in our triangle, we'll notice that if we're talking about 1/6 of pi the side opposite to it is the side with one unit. OK? And the side adjacent to it is the side with the square root of three. And we know that our hypotenuse is always opposite the right angle. So now that we know the opposite adjacent and hypotenuse, then we should be able to solve for the sign of 1/6 of pi because that note tells us that the sign of 1/6 of pi, we will be equal to the opposite side, which is one divided by the high party news, which is two. We don't need to simplify this any further. So this tells us then that the sign of 1/6 of pi equals a half. Therefore, the correct answer is answer choice. A thanks a lot for watching everyone. I hope this video helped.

Find each exact function value. See Example 3.
sin π/3

Key Concepts

Unit Circle

Sine Function

Exact Values of Trigonometric Functions

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Find each exact function value. See Example 3.sin π/3

Key Concepts

Unit Circle

Sine Function

Exact Values of Trigonometric Functions

Watch next

Find each exact function value. See Example 3.
sin π/3