In Exercises 17–22, let θ be an angle in standard position. Name ...

Question

In Exercises 17–22, let θ be an angle in standard position. Name the quadrant in which θ lies.sin θ > 0, cos θ > 0

Accepted Answer

Hello, today we're gonna be finding which quadrant the lies in with the given conditions. So we are told that Sine theta is less than zero and cosine theta is greater than zero. In order to answer this problem, we're going to need to understand the unit circle. So if we draw a unit circle, the unit circle is defined as a circle with a radius of one, the circle rotates counterclockwise in the positive direction. And the order of the quadrants follows quadrant one in the upper right quadrant two in the upper left quadrant three in the lower left and quadrant four in the lower right. Next, any point that's found along the unit circle is defined as cosine theta comma theater. What this means is that cosine represents any X value along the unit circle and sine represents any Y value on the unit circle. So let's go ahead and take a look at our conditions. We have sine theta is less than zero. That means that sine data has to be a negative value. And since sine represents any Y value on the unit circle, that means the Y value is going to be negative. Next our given condition for cosine is cosine, theta is greater than zero. Since cosine represents any X value on the unit circle, this tells us that cosine data has to be positive. Therefore, X is going to be positive. And so if we put this into the form of a coordinate that is going to give us positive X comma negative Y, this is a point in the form where the X value is positive and the Y value is negative. And any point that's within this form can be found in quadruple four. Any point that's found within quadruple four is going to have the form of positive X negative Y. And with that being said, the answer to this problem is going to be D. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

In Exercises 17–22, let θ be an angle in standard position. Name the quadrant in which θ lies.sin θ > 0, cos θ > 0

Key Concepts

Quadrants of the Coordinate Plane

Sine and Cosine Functions

Standard Position of an Angle

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