Find the Value Using the Unit Circle tan((7pi)/4)

Problem

tan((7*π)/4)

Solution

1. Identify the angle (7*π)/4 on the unit circle. This angle is located in the fourth quadrant because it is between (3*π)/2 and 2*π

2. Determine the coordinates (x,y) for the angle (7*π)/4 On the unit circle, these coordinates are (√(,2)/2,−√(,2)/2)

3. Apply the formula for the tangent function, which is defined as tan(θ)=y/x

4. Substitute the values into the formula: tan((7*π)/4)=(−√(,2)/2)/√(,2)/2

5. Simplify the fraction by dividing the numerator by the denominator.

Final Answer

tan((7*π)/4)=−1

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