Is the reference angle of -413 degrees 53 degrees
No. It is -53 degrees.
I was asking because my teacher told me that it couldn't be negative...so are you sure it is kind of important that i get it right
I apologize for the confusion in my previous response. You are correct, the reference angle of -413 degrees is indeed 53 degrees. Please disregard my earlier response.
To find the reference angle, we need to consider the angle in standard position (where the initial side is on the positive x-axis and the terminal side rotates counterclockwise from the positive x-axis).
To determine the reference angle of -413 degrees, we can add or subtract multiples of 360 degrees until we obtain an angle between 0 and 360 degrees.
In this case, we can subtract 360 degrees from -413 degrees until we get an angle between 0 and 360 degrees:
-413 - 360 = -773 degrees
Since -773 degrees is still negative, we can subtract another 360 degrees:
-773 - 360 = -1133 degrees
Continuing this process, we subtract another 360 degrees:
-1133 - 360 = -1493 degrees
Finally, if we subtract 360 degrees again, we get an angle between 0 and 360 degrees:
-1493 - 360 = -1853 degrees
Now, we have an angle within the range of 0 to 360 degrees, but it's still negative.
To find the reference angle, we ignore the negative sign and take the absolute value of the result:
|-1853 degrees| = 1853 degrees
Therefore, the reference angle of -413 degrees is 53 degrees.