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For the rotation -152^(@), find the coterminal angle from 0^(@) <= theta < 360^(@), the quadrant, and the reference angle. The coterminal angle is ◻^(@), which lies in Quadrant ◻, with a reference angle of ◻^(@).

For the rotation −152∘ -152^{\circ} , find the coterminal angle from 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} , the quadrant, and the reference angle.\newlineThe coterminal angle is □∘ \square^{\circ} , which lies in Quadrant □ \square , with a reference angle of □∘ \square^{\circ} .

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Q. For the rotation −152∘ -152^{\circ} , find the coterminal angle from 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} , the quadrant, and the reference angle.\newlineThe coterminal angle is □∘ \square^{\circ} , which lies in Quadrant □ \square , with a reference angle of □∘ \square^{\circ} .
  1. Add 360360°: To find the coterminal angle, add 360°360° to −152°-152° until the result is between 0°0° and 360°360°.\newline−152°+360°=208°-152° + 360° = 208°
  2. Check result: Check if 208∘208^\circ is between 0∘0^\circ and 360∘360^\circ.\newlineYes, it is.
  3. Determine quadrant: Determine the quadrant for 208°208°. Since 208°208° is more than 180°180° but less than 270°270°, it's in Quadrant III.
  4. Find reference angle: Find the reference angle for 208°208° in Quadrant III.\newlineReference angle = 180°−(208°−180°)180° - (208° - 180°)\newlineReference angle = 180°−28°180° - 28°\newlineReference angle = 152°152°

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