For the rotation -1053^(@), find the coterminal angle from 0^(@) <= theta < 360^(@), the quadrant, and the reference angle. The coterminal angle is ◻^(@), which lies in Quadrant ◻, with a reference angle of ◻^(@).

Add 360°: To find the coterminal angle, add or subtract multiples of 360° until the angle is between 0° and 360°. -1053° + 360° = -693°Keep adding 360°: Keep adding 360° until the angle is positive. -693° + 360° = -333°Add 360°: Add 360° again. -333° + 360° = 27° Now, 27° is between 0° and 360°, so it's the coterminal angle we're looking for.Identify Quadrant: The coterminal angle 27° lies in Quadrant I because it's between 0° and 90°.Find Reference Angle: The reference angle is the acute angle formed by the terminal side of the angle and the x-axis. Since 27° is already in Quadrant I and is acute, the reference angle is the same as the coterminal angle: 27°.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

For the rotation
-1053^(@), find the coterminal angle from
0^(@) <= theta < 360^(@), the quadrant, and the reference angle.
The coterminal angle is
◻^(@), which lies in Quadrant
◻, with a reference angle of
◻^(@).

For the rotation $-1053^{\circ}$ , find the coterminal angle from 0^{\circ} \leq \theta<360^{\circ} , the quadrant, and the reference angle. $\newline$ The coterminal angle is $\square^{\circ}$ , which lies in Quadrant $\square$ , with a reference angle of $\square^{\circ}$ .

View step-by-step help

Home

Math Problems

Precalculus

Find trigonometric ratios using a Pythagorean or reciprocal identity

Full solution

Q. For the rotation

-1053^{\circ}

, find the coterminal angle from

0^{\circ} \leq \theta<360^{\circ}

, the quadrant, and the reference angle.

\newline

The coterminal angle is

\square^{\circ}

, which lies in Quadrant

\square

, with a reference angle of

\square^{\circ}

Add $360$ °: To find the coterminal angle, add or subtract multiples of $360°$ until the angle is between $0°$ and $360°$ . $\newline$ $-1053° + 360° = -693°$
Keep adding $360$ °: Keep adding $360$ ° until the angle is positive. $\newline$ $-693° + 360° = -333°$
Add $360$ °: Add $360$ ° again. $\newline$ $-333° + 360° = 27°$ $\newline$ Now, $27°$ is between $0°$ and $360°$ , so it's the coterminal angle we're looking for.
Identify Quadrant: The coterminal angle $27°$ lies in Quadrant I because it's between $0°$ and $90°$ .
Find Reference Angle: The reference angle is the acute angle formed by the terminal side of the angle and the x-axis. Since $27^\circ$ is already in Quadrant I and is acute, the reference angle is the same as the coterminal angle: $27^\circ$ .