Find each exact function value. See Example 3.
sin 5π/...

Question

Find each exact function value. See Example 3.

sin 5π/6

Accepted Answer

Hello, everyone. We are asked to determine the exact value of the given function. We are given the sine of three pi divided by four. Our answer choices are a, the square root of two divided by two B, the square root of two C one D in parentheses, one plus the square root of two, all of which is divided by two. First looking at the sine of three pi divided by four. I know I'm gonna take three pi divided by four and find a reference angle for it. So I can have it be an acute angle. I do that by doing pi minus three pi divided by four. So this is the same as saying four pi divided by four minus three pi divided by four, which is pi divided by four. So now that I know that pi divided by four is my reference angle. I'm gonna draw a special right triangle using that I recall that pi divided by four is the same as 45 degrees. So I know I have a special rate triangle that was a 45 45 90. So that's what I'm drawing. I put my 90 degree angle in, I'm gonna put pie over four instead of my 40 fives. I'm gonna label this triangle ABC where B is my right angle. And I recall that in a 45 45 90 triangle, the legs have a measure of one and the hypotenuse has a measure of radical too. So now I can say I'm finding the sign of the angle at A and recall that sign is the opposite side divided by the hypotenuse. So the opposite side is side BC in my diagram, the hypotenuse is side AC. So BC has a measure of one AC has a measure of radical two. So currently, I have one divided by the square root of two. I want to rationalize this denominator. So I'm going to multiply both the numerator and the denominator by the square root of two. And I get the square root of two divided by two. So that means the sine of pi divided by four is the square root of two divided by two. And it also means the sign of three pi divided by four is equal to the square root of two divided by two. So that is our answer and it is answer choice. A have a nice day.

Find each exact function value. See Example 3.
sin 5π/6

Key Concepts

Unit Circle

Sine Function

Reference Angles

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