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Find the measure of a negative angle coterminal with 90∘90^\circ.\newline____ ∘\_\_\_\_\,^\circ

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Full solution

Q. Find the measure of a negative angle coterminal with 90∘90^\circ.\newline____ ∘\_\_\_\_\,^\circ
  1. Subtract 360360° from 9090°: To find a negative angle coterminal with 9090°, subtract 360360° from 9090° because coterminal angles are separated by full rotations, which are 360°360°.\newlineCalculation: 90°−360°=−270°90° - 360° = -270°.
  2. Verify −270°-270° is coterminal: Check if −270°-270° is indeed negative and coterminal with 90°90°. Coterminal angles have the same initial and terminal sides when drawn in standard position. Since 90°90° is a quarter turn from the positive x-axis, and −270°-270° is three quarter turns in the negative direction, they end up in the same position.

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