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Evaluating the Tangent Function - Problem 1

Teacher/Instructor Norm Prokup
Norm Prokup

Cornell University
PhD. in Mathematics

Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.

I want to find the value of tangent of 4 pi over 3. Once you know the values of tangent in the first quadrant, you can find the value of any special angle in any quadrant. And the first step is to draw a diagram, the second step reference angle. The reference angle is this angle, the angle between the x axis and terminal side and it's pi over 3.

Then I have to take the tangent of that angle, tangent of pi over 3 and I remember that from the first quadrant it's root 3. Then I need to decide whether tangent is positive or negative in the third quadrant and from the memory device 'all student students take calculus', tangent is positive in the third quadrant, so the tangent of 4 pi over 3 will equal the square root of 3 exactly.

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