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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