In Exercises 8–12, draw each angle in standard position. -135°...

Question

In Exercises 8–12, draw each angle in standard position. -135°

Accepted Answer

Welcome back. I am so glad you're here. We are asked to sketch the given angle note that the angle should be in standard position. Our given angle is negative 105 degrees. All right, dealing with standard position. That means we're dealing with a rectangular coordinate plane. So we can draw a rough sketch of that. We'll have a vertical Y axis, a horizontal X axis. They come together at the origin in the middle, our angle is in standard position. That means its initial side is the positive side of the X axis. So from the origin extending out toward positive infinity along the X axis and the vertex is at the origin. So that's what we know about Standard position. What else do we know? Well, we've got a negative 105 degrees. This negative part means that we are going to be turning clockwise from our initial side. All right. And it's 105 degrees clockwise. So where's 105 degrees? Well, we recall from previous lessons that if we go all the way from the x axis, we're heading clockwise down to the y axis, the y axis, the negative side of it would be a 90 degrees, a negative 90 degrees. And then if we kept going clockwise back to the negative side of the X axis, that would be a negative 180 degrees. So for our angle of negative 105 degrees, that's just going to be 15 degrees past the Y axis in the third quadrant. So from the origin where our vertex is, we can draw our line heading toward negative infinity for X and Y closer to the Y axis than toward the x axis. And there is our angle well done. We'll catch you on the next one.

In Exercises 8–12, draw each angle in standard position. -135°

Key Concepts

Standard Position of an Angle

Measuring Negative Angles

Quadrants and Angle Placement

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