CONCEPT PREVIEW Match each trigonometric function value or angle ...

Question

CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II.

I                                  II.
1.                               A. 88.09084757°
2.                               B. 63.25631605°
3.                               C. 1.909152433°
4.                               D. 17.45760312°
5.                               E. 0.2867453858
6.                               F. 1.962610506
7.                               G. 14.47751219°
8. tan⁻¹ 30                  H. 1.015426612
9.                                I. 1.051462224
10.                             J. 0.9925461516

Accepted Answer

Welcome back. Everyone. In this problem, we want to evaluate the trigonometric expression of the arc tangent of 54 using a calculator. And we want to approximate our answer to three decimal places for our answer choices. A is 88.394. B is 98.129 C is 98.821 and D is 88.939. And all of our answers are written in degrees. Now, before we evaluate, ensure that your calculator is in degree mode typically to find the arc tangent, you will often see on your calculator, the tangent button and you can press the shift button and that typically gives you the arc tangent, but it's not the same for all calculators, but that's how it goes for most. So when you find the arc tangent of 54 you will notice that it should give you 88.93908830974. And some calculators continue on, but that's not what we want. We want to approximate our answer to three decimal places. So to three decimal places, our third decimal digit is nine beside it, our number is less than five. So we can write that as 88.939 degrees to the nearest three decimal places. Now, one thing to note is that our anger is in the first quadrant. If we think about it on our unit circle, our angle would be somewhere right here 88. Or rather, let me write the actual value the arc tangent of 54. But remember the arc tangent function is from negative half of py radians all the way to half of P radians. And if we think about it, we don't expect a value from the fourth quadrant because the tangent function is negative there. Therefore, our only value would have been 88.939 degrees, which when we look in our answer choices would have been answer choice. D Thanks a lot for watching everyone. I hope this video helped.

Key Concepts

Trigonometric Functions

Inverse Trigonometric Functions

Angle Measurement

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