In Exercises 44–48, find the reference angle for each angle.

Question

-410°

Accepted Answer

Hello, today we're gonna be calculating the reference angle for the given angle. So what we are given is negative 435 degrees. Now, one thing to note is that this angle lies outside one rotation of the unit circle, one rotation of the unit circle is defined as 0 to 360 degrees. So what we're gonna wanna do is we're going to want to rewrite the given angle into standard form. And what this means is that we're going to rewrite the angle into an angle that lies between zero and 360 degrees. Note that we have a negative angle. So in order to rewrite this in standard form, we're going to need to add 360 degrees to this given value negative 435 plus 360 is going to give us negative 75 degrees. Now, this angle still lies outside the region of zero and degrees. So we're going to add one more rotation to this angle, which means we're going to add 360 to negative adding these two values together is going to give us the angle measure of 285 degrees. So now we have negative 435 in a standard form which is 285 degrees. So now what we wanna do is we want to locate where 285 degrees lies on the unit circle. So where does 285 degrees lie on the unit circle while 285 is going to exist in the fourth quadrant of the unit circle. And now that we have the location of 285 degrees, we're going to calculate the reference angle. The reference angle lies between the given angle and the x axis. And in order to get a reference angle in quadrant four, we're going to take 360 degrees and subtract our given angle which is 285 degrees. 360 minus 285 is going to give us the value of 75 degrees. And what this means is that 75 degrees is going to be the reference angle to 400 thir negative 435 degrees. And with that being said, the answer to this problem is going to be a. 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 44–48, find the reference angle for each angle.
-410°

Key Concepts

Reference Angle

Coterminal Angles

Quadrants and Angle Positioning

Watch next