Concept Check Suppose that ―90°

Question

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

sec(―θ)

Accepted Answer

Welcome back. Everyone. In this problem, we want to determine whether the value of the function the cosine of negative Q is positive or negative if Q is between negative 90 degrees and 90 degrees. For our answer choices A is positive and B says it's negative. Now, let's think about what we have here. We're dealing with the cosine function. And one of the best ways to visualize it is by using the unit circle. Now, if I draw the unit circle here, then where I have my Y axis and my X axis. What we're trying to figure out is if the values of the cosine are positive or negative between Q being the angle being negative 90 which negative 90 would have been on the negative side of the Y axis and positive 90 which would have been at the positive side of the Y axis. Now, what else do we know? Well, we also know that for the unit circle, we can recall that every coordinate on it is in the form the cosine of theta and the sign of theater where the X coordinate is the cosine and the Y coordinate is the sign value we can also recall that the cosine is an even function. In other words, the core sign of negative Q would be equal to the core sign of positive Q. So now let's think about it. Let's think about it for both ranges. In other words, we want to test if at, let me put that in red here, we want to test whether when our angle Q is between zero and 90 if it's positive and when it's between negative 90 0, if it's positive. Now let's start with it being between zero and 90 which would have been this region here. Well, if you notice this is on the right side of the X axis, so it means that all of the X values which are the cosine of theta would be positive. So therefore, it's positive between zero and 90 degrees. How about zero and negative 90 degrees? Well, it's looking good too because down there, it's also on the right side of the X axis. So it also means that those values are positive as well. Therefore, the function, the cosine of negative Q is positive between negative 90 degrees and 90 degrees, which would have been answer choice. A thanks a lot for watching everyone. I hope this video helped.

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

Key Concepts

Definition and Domain of the Secant Function

Even-Odd Properties of Trigonometric Functions

Sign of Cosine and Secant in the Interval -90° < θ < 90°

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