Write the number of values of x in [0, 2 π] that satisfy the equation sin^2x - cos x = 1/4.

Question

Write the number of values of x in [0, 2 π] that satisfy the equation sin²x - cos x = \(\frac{1}4\).

Answer 1

1 - cos²x - cos x = 0.25 

cos x²x + cos x - 0.75 = 0 

Solving the quadratic equation we get 

cos x = 0.5 

cos x = cos 60° 

x = 2nπ ± \(\frac{π}3\)

x = 60° when n = 0 

And x = 300° when n =1