Find the Quadrant of the Angle -30

Problem

−30^∘

Solution

1. Identify the direction of the angle. Since the angle is negative, it is measured clockwise from the positive x-axis.

2. Determine the range for each quadrant in the clockwise direction. Quadrant IV corresponds to angles between 0^∘ and −90^∘

3. Compare the given angle to the quadrant boundaries. Since −90^∘<−30^∘<0^∘ the angle lies within the fourth quadrant.

4. Alternatively, find the coterminal angle by adding 360^∘

−30^∘+360^∘=330^∘

5. Locate the coterminal angle. An angle of 330^∘ is between 270^∘ and 360^∘ which is in Quadrant IV.

Final Answer

−30^∘* is in Quadrant IV

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