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.

cot s = 0.5022

Accepted Answer

Welcome back. I am so glad you're here. We're told, considering the interval from zero to pi divided by two, find the approximate value of X round the answer to four decimal places. We're given that the cotangent of X equals 0.6837. Our answer choices are answer choice. A 1.9711 answer choice B 1.5997 answer trace C 0.9711 and answer trace D 0.5997. All right. When we know what the exact value of a trigonometric function here, Cotangent is equal to and we're trying to find the measure of the angle. We are going to use our calculators. And typically you'd be just going in and looking for the inverse function button, but there is no inverse function button for cotangent. So we have one step in between. We recall from previous lessons that cotangent is the reciprocal function of tangent. So the tangent of X equals one divided by the cotangent of X. And now we can use substitution. So instead of the cotangent of X here in the denominator, we can put what the cotangent of X is equal to 0.6837. So let's do that. We've got the tangent of X equals one divided by what the cotangent of X is equal to 0.6837. And now we can use the inverse function button on our calculators for the tangent. So, on your calculator, you want to make sure you are in radiance mode, that's very important. And then you want to find the button that looks like or excuse me, not cotangent that looks like tangent raise to the negative one. That's the inverse tangent button. And then it'll give you a parentheses and you put in what the tangent of X is equal to one divided by 0.6837 then close the parentheses and hit enter, you'll get something like 0.97109. It'll keep going. But we're asked to round to four decimal places. So the fourth decimal place here is the zero, it looks to the nine rounds up. So here our X is equal to 0.9711. And we look at our answer choices and that matches with answer choice. C well done. We'll catch you on the next one.

Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
cot s = 0.5022

Key Concepts

Cotangent Function

Inverse Trigonometric Functions

Interval [0, π/2]

Watch next