Question

For the rotation 467 ° , find the coterminal angle from 0 degrees, is less than or equal toθ, is less than 360 degrees. What is the quadrant and the reference angle?

Answer 1

The coterminal angle of 467 degrees within the range of 0 to 360 degrees is 107 degrees, which lies in the second quadrant. The reference angle is 73 degrees.

Step-by-step explanation:

To find the coterminal angle of 467 degrees that is between 0 and 360 degrees, you subtract multiples of 360 degrees until you get an angle within that range. Since 467 - 360 equals 107 degrees, the coterminal angle is 107 degrees. Now, to determine the quadrant where this angle lies, consider that angles between 90 and 180 degrees lie in the second quadrant. Since 107 degrees is within this range, it is in the second quadrant. The reference angle is the acute angle the terminal side makes with the x-axis, which in this case is 180 - 107 = 73 degrees.