Answer:
Here we have the equation:
6*sin²(x) + 2*sin²(x) = 1
and we want to find a solution in the range:
-90° < x < 90°
First, we can take the sin²(x) as a common factor to get:
6*sin²(x) + 2*sin²(x) = (6 + 2)*sin²(x) = 1
8*sin²(x) = 1
now we can divide both sides by 8
sin²(x) = 1/8
now we can apply the square root to both sides:
√(sin²(x) = √(1/8)
sin(x) = √(1/8)
Now remember the inverse sine function, Asin(x)
such that:
Asin( sin(x) ) = sin( Asin(x) ) = x
If we apply that to both sides, we get:
Asin( sin(x) ) = Asin(√(1/8))
x = Asin(√(1/8)) = 20.7°
x = 20.7°
