Find the approximate value of s, to four decimal places, in th...

Question

Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.

cos s = 0.9250

Accepted Answer

Welcome back everyone. In this problem considering the interval, open bracket, zero half of pi closed bracket, find the approximate value of X in the equation. The cosine of X equals 0.7816. And we want to round our answer to four decimal places for our answer choices. A is 0.8972. B is 0.3305 C is 0.7816 and D is 0.6736. Now, what we're trying to figure out here is the possible input value of X that we could use to get a result of 0.7816 when we put it into the cosine function. So to understand how we can solve for the value of X, it helps for us to think about how a function works. So what this function is telling us is that basically we're taking an input value of X applying the cosine function and we're getting a result of 0.7816. So if we want to figure out what value we used, we could have used, we could have done the inverse of the function. In other words, if we do our inverse function here, let me make a better looking arrow, then we'll be able to figure out what value of X that would have been. And the inverse function for the cosine is the inverse cosine. So what does that mean that tells us then that since the cosine of X equals 0.7816 the inverse cosine of 0.7816 will give us the value of X. So we undo the function. So the output becomes the new input. Therefore, X equals the inverse cosine of 0.7816. And no, all we need to do is to put that into our calculator. So let's go ahead and do that. When we put it into our calculator, we will find that X on your calculator screen and remember that our calculator should be in the radiant mode. So if you look at the top of the, in one of the corners on the screen, you should be seeing R ad or wherever else in your calculator. And once it's in radiant mode, and we put our expression into our calculator, we should find that we get X to be approximately equal to 0.673 5696084. No, we're not done yet because our problem wants us to run our answer to four decimal places. So to do that, we go to the fourth decimal place in our value, which is five, we look at the digit beside it, which is greater than five. So we're going to round five up. So that means X would be equal to 0.6736 to four decimal places. We know that that's the only value in the interval between zero and a half of pi therefore, the approximate value of X would be answer choice. D. Thanks a lot for watching everyone. I hope this video helped.

Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
cos s = 0.9250

Key Concepts

Cosine Function

Inverse Trigonometric Functions

Quadrants and Angle Ranges

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