Find the Value Using the Unit Circle tan((3pi)/4)

Problem

tan((3*π)/4)

Solution

1. Identify the angle on the unit circle. The angle (3*π)/4 is located in the second quadrant.

2. Determine the coordinates (x,y) for the angle (3*π)/4 On the unit circle, these coordinates are (−√(,2)/2,√(,2)/2)

3. Apply the formula for the tangent function in terms of x and y

tan(θ)=y/x

4. Substitute the values into the formula.

tan((3*π)/4)=√(,2)/2/(−√(,2)/2)

5. Simplify the fraction. Since the numerator and denominator have the same absolute value but opposite signs, the result is −1

Final Answer

tan((3*π)/4)=−1

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