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For the rotation
1415^(@), 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 $1415^{\circ}$ , 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

1415^{\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}

.

Subtract $360$ degrees: To find the coterminal angle between $0$ and $360$ degrees, we subtract $360$ degrees from $1415$ degrees until the result is within the desired range. $\newline$ $1415 - 360 = 1055$ $\newline$ $1055 - 360 = 695$ $\newline$ $695 - 360 = 335$
Find coterminal angle: The coterminal angle is $335^\circ$ .
Identify Quadrant IV: $335$ degrees is in Quadrant IV because it's between $270$ and $360$ degrees.
Find reference angle: To find the reference angle, we subtract the coterminal angle from $360$ degrees because it's in the fourth quadrant. $\newline$ $360 - 335 = 25$

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