Question

I need help! Please look at the picture and solve it with an explanation!

Answer 1

`\text{Option H : $(\pi)/(3)$ and $(2\pi)/(3)$ only}`

Explanation:

We have

`\sin \theta =( √(3))/(2)\\\\\theta = sin^(-1) ( √(3))/(2)\\\\ =60^\circ \\\\= (\pi)/(3)`

Since sine is positive in first and second quadrants and sine is a parodic function, we will have sin(θ)= √3/2 at sin(π - θ)

π - θ = π - π/3 = 2π/3

Therefore the two possible values for θ in the interval 0 ≤ θ ≤ 2π are
π/3 and 2π/3

Correct choice is Option H

You can verify by using a calculator that both these sine values will result in √3/2 which is approximately 0.866