Find an angle theta coterminal to 1119^(@), where 0^(@) <= theta < 360^(@). Answer:

Divide and Calculate Rotations: To find an angle coterminal to 1119° that is between 0° and 360°, we need to subtract or add multiples of 360° until we get an angle in the desired range. This is because adding or subtracting full rotations (360°) does not change the terminal side of the angle.Subtract Full Rotations: First, we calculate how many full 360° rotations are in 1119° by dividing 1119 by 360. 1119 ÷ 360 = 3.1083... The whole number part of the quotient (3) represents the full rotations.Find Coterminal Angle: Next, we subtract the full rotations from the original angle to find the coterminal angle within the range of 0° to 360°. 1119° - (3 × 360°) = 1119° - 1080° = 39°Final Coterminal Angle: The angle 39° is between 0° and 360°, so it is the coterminal angle to 1119° that we were looking for.

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Find an angle
theta coterminal to
1119^(@), where
0^(@) <= theta < 360^(@).
Answer:

Find an angle $\theta$ coterminal to $1119^{\circ}$ , where 0^{\circ} \leq \theta<360^{\circ} . $\newline$ Answer:

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Math Problems

Algebra 2

Csc, sec, and cot of special angles

Full solution

Q. Find an angle

\theta

coterminal to

1119^{\circ}

, where

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

\newline

Answer:

Divide and Calculate Rotations: To find an angle coterminal to $1119^\circ$ that is between $0^\circ$ and $360^\circ$ , we need to subtract or add multiples of $360^\circ$ until we get an angle in the desired range. This is because adding or subtracting full rotations ( $360^\circ$ ) does not change the terminal side of the angle.
Subtract Full Rotations: First, we calculate how many full $360°$ rotations are in $1119°$ by dividing $1119$ by $360$ . $\newline$ $1119 \div 360 = 3.1083...$ $\newline$ The whole number part of the quotient ( $3$ ) represents the full rotations.
Find Coterminal Angle: Next, we subtract the full rotations from the original angle to find the coterminal angle within the range of $0^\circ$ to $360^\circ$ . $\newline$ $1119^\circ - (3 \times 360^\circ) = 1119^\circ - 1080^\circ = 39^\circ$
Final Coterminal Angle: The angle $39°$ is between $0°$ and $360°$ , so it is the coterminal angle to $1119°$ that we were looking for.