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Find an angle theta coterminal to 645^(@), where 0^(@) <= theta < 360^(@). Answer:

Find an angle θ \theta coterminal to 645∘ 645^{\circ} , where 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} .\newlineAnswer:

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Inverses of sin, cos, and tan: radiansright chevron icon

Full solution

Q. Find an angle θ \theta coterminal to 645∘ 645^{\circ} , where 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} .\newlineAnswer:
  1. 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∘360^\circ). To find a coterminal angle within a specific range, we can add or subtract multiples of 360∘360^\circ from the given angle.
  2. Subtract 360360° from 645645°: Subtract 360360° from 645645° until the result is between 0°0° and 360°360°. Starting with 645°645°, we subtract 360°360°: 645°−360°=285°645° - 360° = 285°. Since 285°285° is between 0°0° and 360°360°, this is a coterminal angle to 645°645° within the desired range.

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