Answer:
x = 88.463°
Step-by-step 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 ,
[tex]\rm\implies\red{ 0^0 < x < 360^0 }[/tex]
Given trigonometric equation :-
[tex]\rm\implies\red{ 1 + 5 sin (x-100^0)=0 }[/tex]
Subtracting 1 both sides , we have ,
[tex]\rm\implies 5sin( x - 100^0)= -1 [/tex]
Divide both sides by 5 ,
[tex]\rm\implies sin( x - 100^0)= \dfrac{-1}{5} [/tex]
This equation can be written as ,
[tex]\rm\implies x - 100^0 =sin^{-1}\bigg(\dfrac{ -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} [/tex]
