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

Problem

tan((4*π)/3)

Solution

1. Identify the angle (4*π)/3 on the unit circle. This angle is located in the third quadrant because π<(4*π)/3<(3*π)/2

2. Determine the coordinates (x,y) for the angle (4*π)/3 On the unit circle, these coordinates are (−1/2,−√(,3)/2)

3. Apply the formula for the tangent function, which is defined as the ratio of the y-coordinate to the x-coordinate.

tan(θ)=y/x

4. Substitute the specific coordinates into the formula.

tan((4*π)/3)=(−√(,3)/2)/(−1/2)

5. Simplify the expression by canceling the denominators and the negative signs.

tan((4*π)/3)=√(,3)

Final Answer

tan((4*π)/3)=√(,3)

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