Find the Exact Value tan(855)

Problem

tan(855)

Solution

1. Find the coterminal angle by subtracting multiples of 360 until the angle is between 0 and 360

855−2*(360)=855−720

855−720=135

2. Identify the quadrant for the angle 135 Since 90<135<180 the angle lies in Quadrant II.

3. Determine the reference angle for 135 in Quadrant II.

(θ_ref)=180−135

(θ_ref)=45

4. Apply the tangent sign for Quadrant II. In Quadrant II, the tangent function is negative.

tan(135)=−tan(45)

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

tan(45)=1

tan(135)=−1

Final Answer

tan(855)=−1

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