Question

For the rotation − 104 3 ∘ −1043 ∘ , find the coterminal angle from 0 ∘ ≤ θ < 36 0 ∘ 0 ∘ ≤θ<360 ∘ , the quadrant and the reference angle.

Answer 1

To find the coterminal angle between 0° and 360° for − 1043°, we add 360° to reach 37° and then subtract 360° to get 323°. This angle is in the fourth quadrant, and the reference angle is 37°.

Step-by-step explanation:

To find a coterminal angle that is between 0° and 360° for a given angle of − 1043°, we can add or subtract multiples of 360° until we land in the desired range. In this case, we add 360° repeatedly until the result is within the specified interval:

− 1043° + 3×360° = − 1043° + 1080° = 37°

Since 37° is greater than 360° we must subtract 360° to bring it back within range:

37° − 360° = − 323°

Therefore, the coterminal angle between 0° and 360° is 323°, which falls in the fourth quadrant. The reference angle can be found by subtracting the angle from 360°, which results in 360° − 323° = 37°.

Answer 2

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Answer:

• co-terminal: 37°
• 1st quadrant
• reference angle: 37°

Step-by-step explanation:

-1043°/360° ≈ -2.9

Adding 3×360° will give a co-terminal angle in the range 0-360°:

-1043° +1080° = 37°

This co-terminal angle is in the first quadrant. It is also the reference angle.