Concept Check Sketch each angle in standard position. Draw an arr...

Question

Concept Check Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ―90 °

Accepted Answer

Hello, everyone. We are asked to plot the given angle in standard position and represent the rotations using an arrow. Then we'll state the quadrant of the angle and also find a positive and negative conterminal angle. So starting in standard position, we are looking at the value negative 270 degrees. Standard position starts on the positive side of the X axis. A negative 270 degrees means we are gonna go clockwise. So we're gonna go down under the X axis and we're going 270 degrees, which is the same as three times 90. So we'll go three quadrants in our negative direction. So starting from our standard position on the X axis, we are rotating clockwise and this point will land on our Y axis. So it lands on the y axis. So it isn't actually in either quadrant. So it has no quadrant. Next, we want to state the quadrant we did that. It does not have one. It is on the y axis finding a positive and negative conterminal angle to find a positive conterminal angle. I can either add degrees to negative 270 degrees because 360 degrees. Recall is one full rotation. Or if I have this graphic like I do here, I can see that the positive co terminal angle would be 90 degrees. But if we don't have a graphic, the easiest way to do this would be to add a full rotation. So negative 270 degrees plus degrees gives us 90 degrees as our positive conterminal angle for our negative conterminal angle, we are gonna subtract one rotation. So we'll do 270 degrees and we're subtracting 360 degrees, meaning we are going one full rotation clockwise versus counterclockwise. And when I subtract those two values, I get a negative 630 degrees. So that is our negative co terminal angle. So graphing it, we plotted it, it goes clockwise, lands on the Y axis. So it's not an either quadrant. A positive conterminal angle is 90 degrees. A negative conterminal angle is negative 630 degrees. Have a nice day.

Concept Check Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. ―90 °

Key Concepts

Standard Position of an Angle

Coterminal Angles

Quadrants of the Coordinate Plane

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