Find the Reference Angle cos(105)

Problem

cos(105^∘)

Solution

1. Identify the quadrant in which the given angle θ=105^∘ lies. Since 90^∘<105^∘<180^∘ the angle is in Quadrant II.

2. Apply the formula for the reference angle θ^′ in Quadrant II. The reference angle is the acute angle formed by the terminal side and the x-axis.

3. Calculate the value using the formula θ^′=180^∘−θ

θ^′=180^∘−105^∘

θ^′=75^∘

Final Answer

Reference Angle of *105^∘=75^∘

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