Find the Quadrant of the Angle cos(105)

Problem

cos(105^∘)

Solution

1. Identify the unit of the angle. Since 105 is typically used in degrees for basic trigonometry unless specified as radians, we treat it as 105^∘

2. Determine the standard ranges for each quadrant in degrees: Quadrant I is 0^∘<θ<90^∘ Quadrant II is 90^∘<θ<180^∘ Quadrant III is 180^∘<θ<270^∘ and Quadrant IV is 270^∘<θ<360^∘

3. Compare the given angle to these ranges. Since 90^∘<105^∘<180^∘ the angle falls within the second quadrant.

4. Verify the sign of the cosine function. In Quadrant II, the xcoordinates are negative, which means cos(105^∘) is negative.

Final Answer

Quadrant of *105^∘=Quadrant II

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