Find an angle theta coterminal to 1180^(@), where 0^(@) <= theta < 360^(@). Answer:

Understand coterminal angles: Understand what a coterminal angle is. Coterminal angles are angles that share the same initial and terminal sides but differ in the number of rotations. To find a coterminal angle within a specific range, we can add or subtract multiples of 360° (a full rotation) from the given angle.Subtract multiples of 360°: Subtract multiples of 360° from 1180° until the result is between 0° and 360°. 1180° - 360° = 820° (still greater than 360°, so subtract another 360°) 820° - 360° = 460° (still greater than 360°, so subtract another 360°) 460° - 360° = 100° (this is between 0° and 360°, so we have found our coterminal angle)Verify result in range: Verify that the result is within the specified range. 100° is indeed between 0° and 360°, so it is a valid coterminal angle to 1180°.

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Find an angle
theta coterminal to
1180^(@), where
0^(@) <= theta < 360^(@).
Answer:

Find an angle $\theta$ coterminal to $1180^{\circ}$ , where 0^{\circ} \leq \theta<360^{\circ} . $\newline$ Answer:

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Math Problems

Algebra 2

Find trigonometric ratios using reference angles

Full solution

Q. Find an angle

\theta

coterminal to

1180^{\circ}

, where

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

\newline

Answer:

Understand coterminal angles: Understand what a coterminal angle is. $\newline$ Coterminal angles are angles that share the same initial and terminal sides but differ in the number of rotations. To find a coterminal angle within a specific range, we can add or subtract multiples of $360^\circ$ (a full rotation) from the given angle.
Subtract multiples of $360$ °: Subtract multiples of $360°$ from $1180°$ until the result is between $0°$ and $360°$ . $\newline$ $1180° - 360° = 820°$ (still greater than $360°$ , so subtract another $360°$ ) $\newline$ $820° - 360° = 460°$ (still greater than $360°$ , so subtract another $360°$ ) $\newline$ $1180°$ $0$ (this is between $0°$ and $360°$ , so we have found our coterminal angle)
Verify result in range: Verify that the result is within the specified range. $100^\circ$ is indeed between $0^\circ$ and $360^\circ$ , so it is a valid coterminal angle to $1180^\circ$ .