Find an angle thetaθ coterminal to 843, degrees843 ∘ , where 0, degrees, is less than or equal to, theta, is less than, 360, degrees0 ∘ ≤θ<360 ∘ .
Question
Find an angle thetaθ coterminal to 843, degrees843 ∘ , where 0, degrees, is less than or equal to, theta, is less than, 360, degrees0 ∘ ≤θ<360 ∘ .
Solution
To find an angle coterminal to 843 degrees in the range of 0 to 360 degrees, you need to reduce 843 by multiples of 360 (since a full circle is 360 degrees) until you get an angle within the desired range.
Step 1: Divide 843 by 360. 843 ÷ 360 = 2.34167
Step 2: Since we only care about full rotations, ignore the decimal and subtract the whole number result from the original angle. 843 - (2 * 360) = 843 - 720 = 123
So, the angle coterminal to 843 degrees, where 0 degrees ≤ theta < 360 degrees, is 123 degrees.
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