To find a positive and a negative angle coterminal with a given angle, you can
add and subtract 360° if the angle is measured in degrees
or 2π if the angle is measured in radians .
How do you find a negative Coterminal angle?
A negative angle moves in a clockwise direction. In this case, to find the negative coterminal angle,
subtract 360° from 30°
. Below is a 30° angle in standard position. This angle opens in a counterclockwise direction.
What is the formula for Coterminal angles?
We can find the coterminal angles of a given angle by using the following formula: Coterminal angles of a given angle θ may be obtained by either adding or subtracting a multiple of 360° or 2π radians. Coterminal of
θ = θ + 360° × k if θ
is given in degrees. Coterminal of θ = θ + 2π × k if θ is given in radians.
What is a positive Coterminal angle of?
In Mathematics, the coterminal angle is defined as an angle, where two angles are drawn in the standard position. Also both have their terminal sides in the same location. For example, the coterminal angle of 45 is 405 and
-315
. Here 405 is the positive coterminal angle, -315 is the negative coterminal angle.
How do you find a positive Coterminal angle?
To find a positive and a negative angle coterminal with a given angle, you can
add and subtract 360° if the angle is measured in degrees
or 2π if the angle is measured in radians .
What is the Coterminal angle of 90?
Coterminal angle of 90° (
π / 2
): 450°, 810°, -270°, -630°
What is the least positive Coterminal angle?
Explanation: 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.
What angles are Coterminal with a 95 angle?
Add 360° 360 ° to −95° – 95 ° . The resulting angle of
265° 265 °
is positive and coterminal with −95° – 95 ° .
What is the standard position of an angle?
Standard Position: An angle is in standard position
if its vertex is located at the origin and one ray is on the positive x-axis
. The ray on the x-axis is called the initial side and the other ray is called the terminal side.
Are reference angles always positive?
The
reference angle is always positive
. In other words, the reference angle is an angle being sandwiched by the terminal side and the x-axis. It must be less than 90 degree, and always positive.
How do you find the Coterminal angle between 0 and 360?
Coterminal angle of 0°: 360°,
720°
, -360°, -720° Coterminal angle of 1°: 361°, 721°, -359°, -719°
How do you find a Coterminal angle between 0 and 2pi?
To get coterminal angles, you simply have to
add or subtract 2π
. In this problem, we are looking for a coterminal angle that is between 0 and 2π , so we will add 2π to −1924π .
Which two angles are both Coterminal with?
| Radians | ✔ Degrees |
|---|
Which two angles are both Coterminal with θ 90?
with
450
, we subtract 360 to get 90, which will satisfy the coterminal angles. For -270, we rotate the pencil to the RIGHT 270 degrees, which will terminate on the 90 degree line, making this satisfy the coterminal angle as well!
What is the Coterminal angle of 120?
Coterminal angle of 120°
(2π / 3): 480°
, 840°, -240°, -600°
Can an angle be Coterminal with itself?
= -2π is an integer multiple of 2π so the given angles are coterminal. π is not an integer multiple of 2π so the given angles are not coterminal. rad and 15◦ represent the same angle and
any angle is coterminal with itself
.
