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For the rotation
-311^(@), 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 $-311^{\circ}$ , 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 $\square^{\circ}$ .

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Write equations of cosine functions using properties

Full solution

Q. For the rotation

-311^{\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 $360$ degrees: To find the coterminal angle between $0$ and $360$ degrees, add $360$ degrees to $-311$ degrees until the result is within the desired range. $\newline$ $-311 + 360 = 49$ degrees.
Identify Quadrant: The coterminal angle is $49$ degrees, which lies in Quadrant I because it's between $0$ and $90$ degrees.
Find Reference Angle: The reference angle for an angle in Quadrant I is the angle itself, so the reference angle is $49$ degrees.

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