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Find an angle theta coterminal to 1036^(@), where 0^(@) <= theta < 360^(@).

Find an angle θ \theta coterminal to 1036∘ 1036^{\circ} , where 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} .

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

Full solution

Q. Find an angle θ \theta coterminal to 1036∘ 1036^{\circ} , where 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} .
  1. Divide by 360360: To find an angle coterminal to 1036∘1036^\circ that lies between 0∘0^\circ and 360∘360^\circ, we need to subtract or add multiples of 360∘360^\circ until the resulting angle is within the specified range.
  2. Subtract Full Rotations: First, we determine how many full rotations of 360°360° are contained in 1036°1036°. We do this by dividing 10361036 by 360360. \newline1036÷360≈2.877...1036 \div 360 \approx 2.877...\newlineThis means that 1036°1036° contains 22 full rotations (since we only consider the whole number part of the division result) and a part of a third rotation.
  3. Find Coterminal Angle: Next, we subtract the full rotations from 1036∘1036^\circ to find the coterminal angle. Since there are 22 full rotations, we subtract 2×360∘2 \times 360^\circ from 1036∘1036^\circ. \newline1036∘−(2×360∘)=1036∘−720∘=316∘1036^\circ - (2 \times 360^\circ) = 1036^\circ - 720^\circ = 316^\circ
  4. Find Coterminal Angle: Next, we subtract the full rotations from 1036∘1036^\circ to find the coterminal angle. Since there are 22 full rotations, we subtract 2×360∘2 \times 360^\circ from 1036∘1036^\circ. \newline1036∘−(2×360∘)=1036∘−720∘=316∘1036^\circ - (2 \times 360^\circ) = 1036^\circ - 720^\circ = 316^\circ The result, 316∘316^\circ, is the coterminal angle to 1036∘1036^\circ that lies between 0∘0^\circ and 360∘360^\circ.

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