Concept Check Suppose that 90°

Question

Concept Check Suppose that 90° < θ < 180° .   Find the sign of each function value. 
 
 cot (θ + 180°)

Accepted Answer

Hello, everyone. We are asked to determine whether the value of the following function is positive or negative. If A is between 90 degrees and 100 80 degrees. So we are given the co tangent of in parentheses, A plus 270 degrees. Our answer choices are a positive B negative. So if we know that the angle A is between 90 degrees and 100 80 degrees, this means that its minimum value is 90 degrees. So let's find out where would this fall for the co tangent if we use our minimum? So our angle would be a plus degrees. So if we're saying it's the minimum, this would be 90 plus 270 degrees just 360 degrees. Since that is a full rotation, we can say that at the minimum, we would be taking the co tangent of 360 degrees, which is the same as saying zero degrees. So we are saying that we take the coat tangent of zero degrees if we're working with the minimum value of 90 degrees for A, so then if we're looking at the maximum value of A, which is 100 80 degrees, we again are gonna do a plus 270 degrees. So if a is 180 degrees plus 270 degrees, this would total 450 degrees. And since again, this is greater than a full rotation, we are going to subtract one rotation to find out what its value would be. If we were just looking at a plane between zero and 360 degrees. So 450 degrees when we subtract a full rotation of 360 degrees is 90 degrees. So this means we'd be looking at the cotangent of 90 degrees. So if our values for our angle that we're taking the cotangent of are at minimum zero degrees and at maximum 90 degrees, this means this is in quadrant one and all trig functions are positive in quadrant one. So our answer is answer choice a positive. Have a nice day.

Concept Check Suppose that 90° < θ < 180° . Find the sign of each function value. cot (θ + 180°)

Key Concepts

Cotangent Function

Angle Addition

Quadrants of the Unit Circle

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