The measure of an angle in standard position is given. Find two positive angles and two negative angles that are coterminal with the given angle. (Enter your answers as a comma-separated list.) 70°

Question

The measure of an angle in standard position is given. Find two positive angles and two negative angles that are coterminal with the given angle. (Enter your answers as a comma-separated list.)

70°

Answer 1

Coterminal is a combination of two things Co = together (as in coworker), and terminal = ending (as in terminal illness). So basically you are finding angles that "end together" or in other words stop at the same place. For this to happen, you'd have to go all the way around the circle, like adding or subtracting 360 degrees, and get back to where you started. In this case, it would be starting at 70 degrees then making full-circle journeys (adding or subtracting 360) in either direction around the circle to get back to 70. So lets do that:

POSITIVE ANSWERS:

1. (one full circle away, clockwise) 70 + 360 = 430 degrees.
2. (two full circles away, clockwise) 70 + 360 + 360 = 790 degrees

NEGATIVE ANSWERS:

1. (one full circle away, counterclockwise) 70 -360 = -290 degrees
2. (two full circles away, counterclockwise) 70 - 360 -360 = -650 degrees

Bonus: As you might have guessed by now, there are an INFINITE amount of coterminal angles for any given angle; all you have to do is keep adding or subtracting full circles (360 when in degrees, or 2 pi when in radians). But to keep things manageable, we will usually only ask you to list a few that are close to the original measurement. In this case it was a maximum of two go-arounds of the circle in either direction.

Answer 2

Positive angles start with an initial side, which is a ray that begins at the origin and follows the x-axis from there on. Positive angles have a terminal side, which is also a ray that begins at the origin and shows the angle to be measured. The measurement is taken in a counter-clockwise direction, and it has either a positive sign or no sign at all.

Negative angles start with an initial side, which is a ray that begins at the origin and follows the x-axis from then on. Negative angles have a terminal side, which is also a ray that begins at the origin and shows the angle to be measured. The measurement is taken in a clockwise direction, and it has a negative sign.

A full circle around the origin is 360 degrees. So 0 degrees and 360 degrees are both the same angle.

To obtain other positive angles, simply add any positive integer multiple of 360 degrees.

70 degrees + 360 degrees is 430 degrees.

70 degrees plus 2×360 degrees = 70 + 720 = 790 degrees

To find a negative (equivalent) angle, simply subtract 360 degrees: 70 - 360 = -290 degrees

If you subtract another 360 degrees, you obtain another equivalent angle: -290 -360 = -650 degrees.

Coterminal angles have the same initial and terminal sides. Their measures are equivalent.