Question

Find the reference angle for the given angle. Show your work. -404°

Answer 1

Answer:

44°

Step-by-step explanation:

The reference angle is the magnitude of the smallest angle between the terminal ray and the x-axis.

Your angle is one full circle clockwise plus 44° more (-360° -44° = -404°), so makes an angle of -44° with respect to the positive x-axis. The magnitude of that is 44°.

_____

Using a function

The attachment shows a calculator function that can be used to find the reference angle for any angle. (Replace the value -404 with the angle of your choice.)

Answer 2

Answer:

44 degrees.

Step-by-step explanation:

What the reference angle is asking for, is that when you rotate that amount of degrees(or radians), you want to find the angle when you connect it to the x-axis. For example, (the attachment) the angle 200 is the same as if you go 20 degrees from the left side of the x axis. So, the same applies if the angle is negative. Also, if you're angle(but it's positive) is bigger than 360, you can just ignore it because it is a full rotation. So 404 is bigger than 360, so we can ignore it. 404-360 is 44. So that means we really rotated -44, meaning we spun clockwise instead of counter clockwise. Now, since our positive angle(44) is less than 90, we are done. This is because if our reference angle is greater then 90, than we can just create a new angle because it would leak into another quadrant, meaning we can define a new reference. Hope this makes sense.