Find the general solutions of the following equations : sin x = 1/2

Question

Find the general solutions of the following equations :

sin x = \(\frac{1}2\)

Answer 1

Ideas required to solve the problem: 

The general solution of any trigonometric equation is given as – 

• sin x = sin y, implies x = nπ + (– 1)ⁿy, where n ∈ Z. 

• cos x = cos y, implies x = 2nπ ± y, where n ∈ Z. 

• tan x = tan y, implies x = nπ + y, where n ∈ Z. 

we have,

sin x = \(\frac{1}2\)

We know that sin 30° = sin π/6 = 0.5 

∴ sinx =  sin\(\frac{π}6\)

∵ it matches with the form sin x = sin y 

Hence

x = nπ + (-1)ⁿ \(\frac{π}3\), where n ϵ Z