Question

Which of the following represents the measures of all angles coterminal with a -200 degree angle?

a) -200 + 360n , where n is an integer
b) -200 - 180n , where n is an integer
c) -200 + 180n , where n is an integer
d) -200 - 360n , where n is an integer

Answer 1

The measures of all angles coterminal with a -200 degree angle are represented by the formula -200 + 360n, where n is an integer (option a). This pattern is due to full rotations of 360 degrees being added to or subtracted from the original angle to find coterminal angles.

Step-by-step explanation:

The angle measures coterminal with a -200 degree angle can be found by adding or subtracting full rotations of 360 degrees. The general formula for determining coterminal angles is the original angle plus or minus 360 degrees multiplied by n, where n is an integer. This can be represented as:

-200 + 360n , where n is an integer

This means that the correct answer for an angle that is coterminal with a -200 degree angle is (a) -200 + 360n, where n is an integer. Whenever n is zero, we get the original angle, and as we increase or decrease n, we find all of the coterminal angles by going in positive or negative full circles.