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.                               H. 1.015426612
9. csc⁻¹ 4                    I. 1.051462224
10.                             J. 0.9925461516

Accepted Answer

Welcome back. Everyone. In this problem, we want to evaluate the trigonometric expression of the arch co count of seven using a calculator. And we want to approximate our answer to three decimal place for our answer choices A is 8.213 degrees. B is 6.976 degrees C is 81.787 degrees and D is 9.126 degrees. No, we can't evaluate our expression for the A cos right away. So we'll need to rewrite the A co in a way that it is one of the typical trick functions, either the sign the cosine or the tangent. Now, let's think about it. What do we know about the? Well, recall that the consequence of an angle is the reciprocal of the sign of that angle? Yeah. So we need to find some way to rewrite the second as the sign of the angle. How can we do that? Well, notice we're dealing with the arc cos, so what do we know about the, and the A cos well, the Ark cos is the inverse function to the. In other words, if you were to take an angle and apply the co to get a ratio, let's call that ratio X. Then if you were to apply the arc cos the inverse function to that ratio, it would give you back the angle. And that's the idea that we're going to use here to figure out the arc cos of seven. So first, let's say that X equals the ark cos of seven. Well, if X is the CO C count of seven, that means the core C count of X must be equal to seven. Recall that the is the reciprocal of the sine function. So that means one divided by the sign of X equals seven, which then tells us that if we reciprocate both terms, the sign of X would be equal to 1/7. No, we still want to find X the, the A count of seven. But we can still use that idea here be because if the sign of X is 1/7 then to find X, we can use the arc sign. In other words, X would be equal to the arc sign off 1/7. Remember that the course the X is the arc co count of seven. So therefore, I can rewrite that here as the A co count of seven equals the arc sign of 1/7. So all we need to do now since sign is an easily available function on our calculators is to find the arc sign of 1/7 and will be and that will be our value. No, the arc sign of 1/7 is 8.213 degrees. So that tells us that the A CO C count of seven equals 8.213 degrees. The angle 8.213 degrees is in the first quadrant. And we don't expect a value from the fourth quadrant because the cos function is negative there. So this would be the only value for the R cos of seven from negative half of P radiant to half of P radiant. When we look in our answer choices, that would have been answer choice. A thanks a lot for watching everyone. I hope this video helped.

Key Concepts

Trigonometric Functions

Inverse Trigonometric Functions

Angle Measurement

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