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Problem 845

# What primary angle is coterminal with the angle of $$1243^{\circ}$$ ?

Expert verified
The primary angle coterminal with the angle $$1243^\circ$$ is $$163^\circ$$.
See the step by step solution

## Step 1: Find the number of full rotations

To determine how many full rotations the given angle goes through, we will divide the angle by $$360^\circ$$. Since we are only concerned with full rotations, we will take the quotient without the remainder. Number of full rotations = $$Q = \frac{1243}{360} \approx 3$$ (ignoring the remainder) This means that the given angle goes through 3 complete rotations and some additional degrees.

## Step 2: Subtract the full rotations from the given angle

We subtract all full rotations from the given angle to obtain the primary angle coterminal with the given angle. Primary angle = $$1243 - (3\times 360) = 1243 - 1080 = 163^{\circ}$$ Thus, $$163^\circ$$ is the primary angle coterminal with the given angle of $$1243^\circ$$.

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