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.                                I. 1.051462224
10. cot⁻¹ 30                J. 0.9925461516

Accepted Answer

Welcome back everyone. In this problem, we want to evaluate the trigonometric expression of the arc core tangent of 60 using a calculator. We also want to approximate our answer to three decimal places for our answer choices A is 0.943 B is 1.061 C is 0. and D is 0.955. And all of these are expressed in degrees. Now, we're working with the arc cotangent, but we can't evaluate this expression right away. So we'll need to re rewrite it or transform it in terms of another readily avai available trick function that is either the sign cosine or tangent function. Now, what do we know about the core tangent? Well, recall that the core tangent is actually the reciprocal of the tangent. So if we can rewrite the arc core tangent in terms of the tangent, then we'll be able to evaluate our expression. But this is talking about the core tangent, not the arc core tangent. So how can we relate both of those will again recall that the A core tangent is the inverse trigonometric function to the core tangent in other words, if I have an angle and I find a core tangent of that angle, then it's going to give me a ratio. If I wanted to take that ratio and figure out the angle that gave me that ratio, then I would use the arc cotangent function. So it undoes the cotangent function. So one thing that we know is that if we have the cotangent of a function theta being equal to X, then the Anger Theater will be equal to the arc cotangent of X. And we can use that relationship here to help us. Because what that tells us then is that if we let, let's let X be equal to the Ark core tangent of 60. OK, then that means by our definition here, the cotangent of X would be equal to 60. Now, if that's the case recall, as we know that the core tangent is the reciprocal of the tangent. So we can rewrite the core tangent of X as the reciprocal of the tangent of X equals 60. If we reciprocate both sides of our equation, that means the tangent of X equals 1/60. And if the tangent of X equals 1/60 then that means X, what we had started out with the, in the arc tangent of 60 would be equal to the inverse tangent of 1/60. So the arc cotangent of 60 equals the arc tangent of 1/60. No, the arc tangent is an easier function to work with. Because on our calculators, we can find the arc tangent by looking for the tangent button and pressing it along with shift. That's how most calculators work. And that typically gives you the arc tangent. It might be different for your calculator, but that's usually how it is. So putting the art tangent of 1/60 in your calculator, you're supposed to get the value 0.95484125387. And it continues on degrees. But remember if we look back in our problem, we only wanted our answer to three decimal places. So if we round our number to three decimal places, the third decimal place is at four be to the right of four, the digit is greater than five. So we can rewrite it at 0. degrees. So that is what the arco tangent of 60 would be equal to, to three decimal places. One thing to note is that the range of the arc cotangent function is from zero radiance to pi radiant. In other words, zero degrees to 180 degrees. So if we think about it on our unit circle, the a cotangent ranges from zero degrees to degrees or a 0.955 degrees, which would probably be somewhere right there is in the first quadrant. And we don't expect that value from the second quadrant because the core second function would be negative in our second quadrant. Therefore, 0.955 degrees would be our only possible value which when we look in our a answer choices, that would have been answer choice. D Thanks for watching everyone. I hope this video helped.

Key Concepts

Trigonometric Functions

Inverse Trigonometric Functions

Angle Measurement

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