Question

Find the principal solution, sinx=1/2

Answer 1

x=30 degrees or $\pi /6$

Answer 2

Given:

• sin(x) = 1/2

To Find:

• The principal solutions of sin(x).

Solution:

We know that

sin(30°) = 1/2 ⇒ sin(π/6) = 1/2

We have a formula in trigonometry which says that

sin(180°-x) = sin(x) ⇒ sin(π-x) = sin(x)

Substitute the value of "x=π/6" in the above equation, we get

⇒ sin(π-π/6) = 1/2

⇒ sin((6π-π)/6) = 1/2  ( Took the LCM of LHS)

⇒ sin(5π/6) = 1/2 → {equation 2}

Equation 2 implies that

• π/6  lies inbetween 0 and 2π
• 5π/6 lies inbetween 0 and 2π

∴ x = π/6 and x = 5π/4 are the principal solutions.

∴ The principal solutions of sin(x) are π/6 and 5π/6.