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Find an angle
theta coterminal to
-424^(@), where
0^(@) <= theta < 360^(@).
Answer:

Find an angle $\theta$ coterminal to $-424^{\circ}$ , where $0^{\circ} \leq \theta<360^{\circ}$ . $\newline$ Answer:

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Find trigonometric ratios using a Pythagorean or reciprocal identity

Full solution

Q. Find an angle

\theta

coterminal to

-424^{\circ}

, where

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

.

\newline

Answer:

Add $360$ degrees: To find an angle coterminal to $-424$ degrees that is between $0$ and $360$ degrees, we need to add or subtract multiples of $360$ degrees until we get an angle in the desired range. Since $-424$ degrees is negative, we will add $360$ degrees until we are within the range of $0$ to $360$ degrees.
Add $360$ degrees: First, add $360$ degrees to $-424$ degrees to get a new angle. $\newline$ $-424$ degrees $+$ $360$ degrees $=$ $-64$ degrees $\newline$ This angle is still negative, so we need to add $360$ degrees again.
Check range: Add $360$ degrees to $-64$ degrees to get the coterminal angle. $\newline$ $-64$ degrees $+$ $360$ degrees $=$ $296$ degrees $\newline$ This angle is now within the desired range of $0$ to $360$ degrees.
Final coterminal angle: Check to ensure that $296$ degrees is indeed between $0$ and $360$ degrees. $\newline$ $0$ degrees $\leq$ $296$ degrees $<$ $360$ degrees $\newline$ This is true, so $296$ degrees is the coterminal angle we were looking for.

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