Find all values of θ, if θ is in the interval [0°, 360°) and has ...

Question

Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. See Example 6.               √3cot θ = - ——                3

Accepted Answer

Hey, everyone here we are asked to determine all possible values of theta in the interval from zero degrees to 360 degrees which have the same value as the given function value. Here we are given cotangent of theta is equal to the square root of three. Here we have four answer choice options. Answer choice A beta is equal to 30 degrees, 150 degrees, 210 degrees or degrees. Answer B beta is equal to 30 degrees, 150 degrees or 210 degrees. Answer C theta is equal to 30 degrees or 210 degrees and answer D beta is equal to 30 degrees or degrees. Now, our first step in this problem is to recall that cotangent of theta has the equivalent ratio of X divided by Y. And now we just need to notice that our given value for cotangent of theta is positive. So that tells us that our ratio X divided by Y must be positive. And we know that this ratio can only be positive when we are in the first or the third quadrant. So this tells us we will have two values of theta, one which will lie in the first quadrant and the other, which lies in the third quadrant. So beginning in the first quadrant, we just need to recall that cotangent of degrees gives us the square root of three. And so we already know that one value of theta will be 30 degrees because it lies in the first quadrant. And now finding our third quadrant value, we have cotangent of 30 degrees is equivalent to cotangent of 180 degrees. And now we need to add 30 degrees in order to make, make it equivalent as well as make it lie in the third quadrant. And so now just simplifying, we have cotangent of 210 degrees and we know that this expression is equivalent to the square root of three. And with this, we have found our second value of theta as degrees. So now again, we have two values of data. The first which lies in the first quadrant and which is degrees and the other, which lies in the third quadrant as 210 degrees. So with this, we have found our two values of theta. And so we are left with answer choice C where again, theta is equal to 30 degrees or degrees. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. See Example 6. √3cot θ = - —— 3

Key Concepts

Cotangent Function

Quadrants of the Unit Circle

Reference Angles

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