Question

What is the value of the expression? tan 5π3

Answer 1

`tan((5\pi)/(3))=√(3)`

Explanation:

we are given

`tan((5\pi)/(3))`

we know that

`tan(x)=(sin(x))/(cos(x))`

so, we can write our expression as

`tan((5\pi)/(3))=(sin((5\pi)/(3)))/(cos((5\pi)/(3)))`

now, we can use unit circle

`sin((5\pi)/(3))=-(√(3) )/(2)`

`cos((5\pi)/(3))=-(1)/(2)`

now, we can plug values

`tan((5\pi)/(3))=(-(√(3) )/(2))/(-(1)/(2))`

`tan((5\pi)/(3))=√(3)`