Coterminal Angles - Trigonometry

The coterminal angle is the negative angle that travels from from the original angle.

To find a coterminal angle, you must add or subtract . The question is asking for the least positive coterminal angle, so you must add until you reach a positive angle.

The angle is still negative, so you must continue.

The angle is still negative, so you must continue.

The angle is still negative, so you must continue.

Coterminal angles are angles in standard position that have a common terminal side. In order to find a positive and a negative angle coterminal with , we can add and subtract . So we can write:

So a angle and a angle are coterminal with a angle.

Coterminal angles are angles in standard position that have a common terminal side. In order to find a positive and a negative angle coterminal with , we can add and subtract . So we can write:

So a angle and a angle are coterminal with a angle.

Coterminal angles are angles in standard position that have a common terminal side. In order to find a positive and a negative angle coterminal with , we need to subtract one full rotation () and two full rotations ():

So a angle and a angle are coterminal with a angle.

Coterminal angles are angles in standard position that have a common terminal side. In order to find a positive and a negative angle coterminal with , we need to subtract one full rotation () and two full rotations ():

So a angle and a angle are coterminal with a angle.

Coterminal angles are angles in standard position that have a common terminal side. In order to find a positive and a negative angle coterminal with , we can add and subtract . So we can write:

So a angle and a angle are coterminal with a angle.

Coterminal angles are angles in standard position that have a common terminal side.

So of the given pairs only is the correct pair.

In order to examine the given pairs we can add to an angle or subtract from an angle:

Coterminal angles share a common side when both are in standard position.

Thus, to find a coterminal angle for , add to it to get a coterminal angle of .

To determine a coterminal angle we must add to the original angle. In order to find the smallest positive coterminal angle, we add until we obtain the first positive angle. We first need to find the least common denominator as follows:

In order to determine a coterminal angle we add or subtract a multiple of . In this case since the angle is positive and we want the nearest negative coterminal angle, we subtract until we obtain the first negative angle as follows:

In order to find a coterminal angle we must either subtract or add multiples of . To find the nearest positive coterminal angle we add :

To determine the nearest negative coterminal angle we subtract :

To find a possible coterminal angle, add or subtract multiples of 360 degrees, or radians. In this case, since we are given the angle in radians, add or subtract .

These are all possible coterminal angles.

The correct answer is:

For an angle to to coterminal with , it must be equivalent to that angle, pointing up. The two angles that work are and .

We can visualize why works in a couple different ways. If we know that the angle pointing straight down is , we can see that the negative version of that would point straight up. We could also count clockwise around the circle three -angles, which would place us at .

Similarly, counting around the unit circle nine -angles would place us at . We could also subtract , or equivalently , to figure out where the angle is within the unit circle:

To obtain any angle that is coterminal with , either add or subtract , or in this case its equivalent, .

Adding yields:

Subtracting yields:

The only answer not generated either way is .

To obtain any angle that is coterminal with , either add or subtract , or in this case its equivalent, .

Adding yields:

Subtracting yields:

The only answer not generated either way is .

Coterminal angles have the same initial and terminal sides. The simplest case is 180°. If you imagine this on a cartesian plane, it is simply the x-axis. The 180° on the positive y-axis side is coterminal with the 180° on the negative y-axis side and vice versa. For an angle of 390° we find its positive coterminal angle by subtracting 360°. This gives us the coterminal angle of 30°. 30° and 390° both have the same initial and terminal sides.

Coterminal angles have the same initial and terminal sides. The simplest case is 180°. If you imagine this on a cartesian plane, it is simply the x-axis. The 180° on the positive y-axis side is coterminal with the 180° on the negative y-axis side and vice versa. To find the negative coterminal angle of 380°, we must subtract an angle that has the same terminal and initial sides, but is larger than 380° (this ensures we get a negative coterminal angle).

To find the correct "amount of angle" to subtract, multiply 360 by multiples of 2 until you get an angle value that would give a negative angle when subtracted.

Adding the two fractions together yields

We can find angles coterminal to this by adding or subtracting multiples of .
In this case:

.

"Coterminal angles" are those angles in standard position that have a common terminal side. To find an angle coterminal to another given angle, simply add or subtract (or ) to the given angle measure. The problem restricts the desired coterminal angles to those which lie between and . Hence, for each given angle measure we must find the angle between and which is equivalent to that angle by adding or subtracting multiples of or .

is negative, so is coterminal to and lies between and .

is greater than , so is coterminal to and lies between and .

is greater than , so is coterminal to and lies between and .

Hence, the positive angles between and which are coterminal to , , and are , , , respectively.