Question

Solve each trigonometric equation such that 0 ≤ x ≤ 2????. Give answers in exact form.

a. 2 sin(x) + √3 = 0
b. tan2(x) − 1 = 0

Answer 1

(a)
`x=(5\pi )/(3)`

(b)
`x=(\pi )/(8)`

Explanation:

It is given that
`0\leq x\leq 2\pi`

(a) We have given equation
`2sinx+√(3)=0`

`sinx=(-√(3))/(2)`

`x=sin^(-1)(-0.866)`

`x=(-\pi )/(3)=2\pi -(\pi )/(3)=(5\pi )/(3)`

(b)
`tan(2x)=1`

`2x=tan^(-1)1`

`2x=(\pi )/(4)`

`x=(\pi )/(8)`