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Find an angle theta coterminal to 1011^(@), where 0^(@) <= theta < 360^(@). Answer:

Find an angle θ \theta coterminal to 1011∘ 1011^{\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 1011∘ 1011^{\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 until the result is within the desired range.
  2. Subtract multiples: Subtract multiples of 360°360° from 1011°1011° until the result is between 0°0° and 360°360°.\newlineSince 1011°1011° is greater than 360°360°, we will subtract 360°360° repeatedly until we get a result within the specified range. We can calculate the number of full rotations by dividing 10111011 by 360360 and then taking the floor of that number.\newlineNumber of full rotations = floor(1011360)=floor(2.8083)=2\text{floor}(\frac{1011}{360}) = \text{floor}(2.8083) = 2
  3. Calculate coterminal angle: Calculate the coterminal angle.\newlineNow we subtract the number of full rotations 2×360°2 \times 360° from the original angle 1011°1011°:\newline1011°−(2×360°)=1011°−720°=291°1011° - (2 \times 360°) = 1011° - 720° = 291°
  4. Verify result: Verify that the result is within the specified range.\newlineWe need to ensure that the coterminal angle we found, 291∘291^\circ, is between 0∘0^\circ and 360∘360^\circ. Since 291∘291^\circ is within this range, we have found our coterminal angle.

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