Question

Question #f620d

Answer 1

`0^@ ; 70^@53` for [0, 90]

Explanation:

`3sin^2 x + 4cos x - 4 = 0`
Replace `sin^2 x` by `(1 - cos^2 x)`
`3 - 3cos^2 x + 4cos x - 4 = 0`, or by changing side:
`3cos^2 x - 4cos x + 1 = 0.`
Since a + b + c = 0, use shortcut. The 2 real roots are:
cos x = 1 and `cos x = c/a = 1/3`
a. cos x = 1 --> x = 0, x = 180, and x = 360.
b. `cos x = 1/3`
Calculator and unit circle give 2 solutions:
`x = +- 70^@53`
Inside the interval [0, 90], there are only 2 solutions:
x = 0, and `x = 70^@53`