Question

Finding the value of this tangent function without a calculator?

tan((2 * PI) / 3)

I know that it is sin((2 * PI) / 3) / cos((2 * PI) / 3) but I do not know how to find the values without a calculator.

Answer 1

sin(2pi/3) = 0.5 * sqrt(3)
cos(2pi/3) = -0.5
so tan(2pi/3) = -sqrt(3)

You need to memorize the unit circle for this sort of problem. It's probably in your textbook.

Answer 2

Thanks! I'll look in my textbook again.