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Find an angle theta coterminal to -253^(@), where 0^(@) <= theta < 360^(@). Answer:

Find an angle θ \theta coterminal to −253∘ -253^{\circ} , where 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} .\newlineAnswer:

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Full solution

Q. Find an angle θ \theta coterminal to −253∘ -253^{\circ} , where 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} .\newlineAnswer:
  1. Add 360360 degrees: To find a coterminal angle, we can add or subtract multiples of 360360 degrees (a full circle) to the given angle until the result is within the desired range of 00 to 360360 degrees.
  2. Find positive coterminal angle: Since −253-253 degrees is negative, we will add 360360 degrees to it to find a positive coterminal angle.\newline−253-253 degrees + 360360 degrees = 107107 degrees
  3. Check within range: Now we check if 107107 degrees is within the range of 00 to 360360 degrees.\newline00 degrees ≤\leq 107107 degrees << 360360 degrees\newlineThis is true, so 107107 degrees is a coterminal angle to −253-253 degrees within the specified range.

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