Find the Exact Value tan(-315 degrees )

Problem

tan(−315)

Solution

1. Find a coterminal angle by adding 360 to the given negative angle to find its equivalent position within the first rotation.

θ=−315+360=45

2. Identify the reference angle and the quadrant. Since 45 is in the first quadrant, the reference angle is 45 and all trigonometric functions are positive.

tan(−315)=tan(45)

3. Evaluate the tangent using the known values for special angles, where tan(45)=1

tan(45)=1

Final Answer

tan(−315)=1

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