Question

Solve each trigonometric equation such that 0 ≤ x ≤ 2????. Round to three decimal places when necessary.

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

Answer 1

(A)
`(\pi )/(3)`

(b)
`1.768\pi`

Explanation:

It is given in the question that
`0\leq x\leq 2\pi`

(a) We have given equation
`2cosx-1=0`

`cosx=(1)/(2)`

`x=cos^(-1)(1)/(2)`

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

(b)
`3sinx+2=0`

`sinx=(-2)/(3)`

`x=sin^(-1)(-0.666)`

`x=-41.75^(\circ)=360-41.75=318.25^(\circ)=1.768\pi`