Find each exact function value. See Example 3.
tan π/4...

Question

Find each exact function value. See Example 3.

tan π/4

Accepted Answer

Welcome back, everyone. In this problem, we want to determine the exact value of the given function of the 10 of a third of Pi. For our answer choices A is the square root of three divided by two, B is two, C is a half and D is a square root of three. Now, if we're going to determine the exact value of the tangent of a third of pi, it would be helpful to think about the right triangle that this given function is in. Now, we noticed that it's a third of pi. So let's ask ourselves, do we know any triangle that has a third of pi in it? Well, we know the special triangle and the special triangle otherwise called the 3060 triangle where a third of pi radiance is 60 degrees and 1/6 of pi radiance is 30 degrees. Tells us that for this right triangle, if we have one of the sides being one, the hypotenuse being two, then the other side will be the square root of three where 1/6 of Pi will be opposite to the side that is one unit and a third of Pi will be opposite to the side, that is the square root of three units. And this is important because a third of pi radians and 1/6 of pi radiance pops up very regularly. So it's good to know the basic triangle that describes these functions, know that we have the right triangle. Then we should be able to find a tangent of a third of pie because we can that the tangent off and go OK. Is he equal to the opposite side of its right triangle divided by its hypotenuse? Now, if we look at our triangle here, we should be able to label it in terms of the opposite adjacent and hyper tenuous. If we're talking about the angular third of pi, then the square root of three will be the opposite side. One will be the adjacent side. Sorry. OK. Let me clear that up one will be the adjacent side and the two will be the side with the high party news, which makes sense because the high party news is always opposite, the right angle know that we know our sides. We should be able to find a tangent of a third off by because now this tells us that the tangent of a third of pie will be equal to the opposite side, which is the square root of three divided by the adjacent side, which is one and the square root of three divided by one equals the square root of three. Therefore, the tangent of a third of pi equals the square root of three. And when we look back in our answer choices, that would have been answer choice. D Thanks a lot for watching everyone. I hope this video helps.

Find each exact function value. See Example 3.
tan π/4

Key Concepts

Trigonometric Functions

Unit Circle

Exact Values of Trigonometric Functions

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