Find the Reference Angle -105 degrees

Problem

−105^∘

Solution

1. Find the coterminal angle between 0^∘ and 360^∘ by adding 360^∘ to the given negative angle.

−105^∘+360^∘=255^∘

2. Determine the quadrant where the angle 255^∘ lies. Since 180^∘<255^∘<270^∘ the angle is in Quadrant III.

3. Apply the reference angle formula for Quadrant III, which is θ^′=θ−180^∘

θ^′=255^∘−180^∘

4. Calculate the result to find the acute angle formed with the x-axis.

255^∘−180^∘=75^∘

Final Answer

Reference Angle of −105^∘=75^∘

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