Find an angle theta coterminal to 1011^(@), where 0^(@) <= theta < 360^(@). Answer:

Understand coterminal angles: Understand the concept of coterminal angles. Coterminal angles are angles that share the same initial and terminal sides but may differ by any number of full rotations (360°). To find a coterminal angle within a specific range, we can add or subtract multiples of 360° from the given angle until the result is within the desired range.Subtract multiples: Subtract multiples of 360° from 1011° until the result is between 0° and 360°. Since 1011° is greater than 360°, we will subtract 360° repeatedly until we get a result within the specified range. We can calculate the number of full rotations by dividing 1011 by 360 and then taking the floor of that number. Number of full rotations = floor(1011 / 360) = floor(2.8083) = 2Calculate coterminal angle: Calculate the coterminal angle. Now we subtract the number of full rotations (2 * 360°) from the original angle (1011°): 1011° - (2 * 360°) = 1011° - 720° = 291°Verify result: Verify that the result is within the specified range. We need to ensure that the coterminal angle we found, 291°, is between 0° and 360°. Since 291° is within this range, we have found our coterminal angle.

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Find an angle
theta coterminal to
1011^(@), where
0^(@) <= theta < 360^(@).
Answer:

Find an angle $\theta$ coterminal to $1011^{\circ}$ , where 0^{\circ} \leq \theta<360^{\circ} . $\newline$ Answer:

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Algebra 2

Inverses of sin, cos, and tan: radians

Full solution

Q. Find an angle

\theta

coterminal to

1011^{\circ}

, where

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

\newline

Answer:

Understand coterminal angles: Understand the concept of coterminal angles. Coterminal angles are angles that share the same initial and terminal sides but may differ by any number of full rotations ( $360^\circ$ ). To find a coterminal angle within a specific range, we can add or subtract multiples of $360^\circ$ from the given angle until the result is within the desired range.
Subtract multiples: Subtract multiples of $360°$ from $1011°$ until the result is between $0°$ and $360°$ . $\newline$ Since $1011°$ is greater than $360°$ , we will subtract $360°$ repeatedly until we get a result within the specified range. We can calculate the number of full rotations by dividing $1011$ by $360$ and then taking the floor of that number. $\newline$ Number of full rotations = $\text{floor}(\frac{1011}{360}) = \text{floor}(2.8083) = 2$
Calculate coterminal angle: Calculate the coterminal angle. $\newline$ Now we subtract the number of full rotations $2 \times 360°$ from the original angle $1011°$ : $\newline$ $1011° - (2 \times 360°) = 1011° - 720° = 291°$
Verify result: Verify that the result is within the specified range. $\newline$ We need to ensure that the coterminal angle we found, $291^\circ$ , is between $0^\circ$ and $360^\circ$ . Since $291^\circ$ is within this range, we have found our coterminal angle.