Question

Given that sin 50ᵒ = 0.766, find two angles x such that sin x = - 0.766, 0ᵒ ≤ x ≤ 360ᵒ

Answer 1

Given

$:\implies \tt \: sin50\degree \: = 0.766$

We know,

sinx < 0, in third and fourth quadrant.

We know,

$:\implies \tt \: sin(180\degree \: + x) = - sinx$

and

$:\implies \tt \: sin(360\degree \: - x) = - sinx$

So,

If

$:\implies \tt \: sinx = - 0.766$

$:\implies \tt \: x = 180\degree \: + 50\degree \: \: \: or \: \: 360\degree \: - 50\degree \:$

$:\implies \tt \: x = 230\degree \: \: \: or \: \: 310\degree \:$