Question

What is the value of the expression? tan 5π3

Answer 1

Answer:

$tan(\frac{5\pi}{3})=\sqrt{3}$

Step-by-step explanation:

we are given

$tan(\frac{5\pi}{3})$

we know that

$tan(x)=\frac{sin(x)}{cos(x)}$

so, we can write our expression as

$tan(\frac{5\pi}{3})=\frac{sin(\frac{5\pi}{3})}{cos(\frac{5\pi}{3})}$

now, we can use unit circle

$sin(\frac{5\pi}{3})=-\frac{\sqrt{3} }{2}$

$cos(\frac{5\pi}{3})=-\frac{1}{2}$

now, we can plug values

$tan(\frac{5\pi}{3})=\frac{-\frac{\sqrt{3} }{2}}{-\frac{1}{2}}$

$tan(\frac{5\pi}{3})=\sqrt{3}$