Find the Exact Value tan(315)

Problem

tan(315)

Solution

1. Identify the reference angle by finding the difference between the given angle and 360 since 315 is in the fourth quadrant.

(θ_ref)=360−315

(θ_ref)=45

2. Determine the sign of the tangent function in the fourth quadrant. In the fourth quadrant, the xcoordinate is positive and the ycoordinate is negative.

tan(θ)=y/x

tan(315)<0

3. Evaluate the tangent of the reference angle using known trigonometric values.

tan(45)=1

4. Combine the value and the sign to find the exact value of the original expression.

tan(315)=−1

Final Answer

tan(315)=−1

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