Question

What is the exact value in degrees 2sin^2x+9cosx-6=0

Answer 1

x = 60 degrees

or

x = 300 degrees

Explanation:

Here, we want to get the exact value of x in degrees

Recall;

sin^2x = 1 - cos^x

Thus, we have that;

2(1 - cos^2x )+ 9cos x - 6 = 0

let cos y = 0

2-2y^2 + 9y -6 = 0

-2y^2 + 9y -4 = 0

-2y^2 + 8y + y - 4 = 0

-2y(y - 4) + 1(y-4) = 0

(1-2y) (y-4) = 0

1 = 2y

y = 4

so y = 1/2 or 4

Since the value of cos cannot be 4, we simply disregard and have y = 1/2 as the only answer

Recall;

y = cos x

cos x = 1/2

x = arc cos 1/2

x = 60 or 300 degrees