Find the Value Using the Unit Circle tan((7pi)/6)

Problem

tan((7*π)/6)

Solution

1. Identify the angle (7*π)/6 on the unit circle. This angle is located in the third quadrant because π<(7*π)/6<(3*π)/2

2. Determine the coordinates (x,y) for the angle (7*π)/6 On the unit circle, these coordinates are (−√(,3)/2,−1/2)

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

4. Substitute the coordinates into the formula:

tan((7*π)/6)=(−1/2)/(−√(,3)/2)

5. Simplify the fraction by canceling the denominators and the negative signs:

tan((7*π)/6)=1/√(,3)

6. Rationalize the denominator by multiplying the numerator and denominator by √(,3)

tan((7*π)/6)=√(,3)/3

Final Answer

tan((7*π)/6)=√(,3)/3

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