Concept Check Suppose that ―90°

Question

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

Accepted Answer

Hello, everyone. We are asked to determine whether the value of the following function is positive or negative. If M is between zero degrees and 180 degrees, we're given the sign of in parentheses M minus degrees. Our answer choices are a positive B negative. So first, I want to focus on finding what angles we're really working with here. So if I know that M is between zero and 100 80 degrees, I can use this to figure out what are the bounds of my angle. So my minimum angle that we're gonna be using in this function would be at the minimum value of M. So that's zero. So it'd be zero degrees minus 180 degrees. So our minimum value that we're looking at here is a negative degrees. Our maximum value would be taking the maximum of M which is 100 80 degrees, subtracting 180 degrees because that's what we're given in the function and we get zero degrees. So this means we are looking to take the sign of values that are between zero degrees, which would be right on the X axis and negative 180 degrees which is still in the X axis. But on the other side, so our angles that we're looking at cover quadrants two or sorry quadrants three and four. And recall that sine is positive in quadrant one, in quadrant two sign is negative in quadrants three and four. So this means that the sign of in parentheses M minus 180 degrees would be answer choice B negative. Have a nice day.

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