Question

Solve for x: 0⁰ < x< 360⁰

`1 + 5 \sin(x - 10 {0}^(0) ) = 0`
​

Answer 1

x = 88.463°

Explanation:

We are given a trigonometric equation and we need to find out the value of x. The angle x lies between 0° and 360° . That is ,

`\rm\implies\red{ 0^0 < x < 360^0 }`

Given trigonometric equation :-

`\rm\implies\red{ 1 + 5 sin (x-100^0)=0 }`

Subtracting 1 both sides , we have ,

`\rm\implies 5sin( x - 100^0)= -1`

Divide both sides by 5 ,

`\rm\implies sin( x - 100^0)= (-1)/(5)`

This equation can be written as ,

`\rm\implies x - 100^0 =sin^(-1)\bigg(( -1)/(5)\bigg) \\\\\rm\implies x - 100^0 = -11.53^0 \\\\\rm\implies x = 100^0-11.53^0\\\\\rm\implies\boxed{\bf x = 88.463^0}`