I got this far, but now I'm stuck...please help
6cos^2theta - 5cos(theta) + 1 = 0
6cos^2theta - 5cos(theta) = -1
cos(theta) * {6cos(theta) - 5} = -1
how about , let cos(theta) = x
then your equation becomes
6x^2 - 5x + 1 = 0
which factors to
(2x - 1)(3x - 1) = 0
x = 1/2 or x = 1/3
then
cos(theta) = 1/2 or cos(theta) = 1/3
theta = 60º or 300º or theta = 70.5º or 289.5º
To solve the equation 6cos^2(theta) - 5cos(theta) + 1 = 0, you have correctly factored the left side of the equation as:
6cos^2(theta) - 5cos(theta) = -1
Now, let's simplify it further:
cos(theta) * {6cos(theta) - 5} = -1
To solve for cos(theta), you need to isolate it on one side of the equation.
Divide both sides of the equation by (6cos(theta) - 5) to obtain:
cos(theta) = -1 / (6cos(theta) - 5)
Now, you have an expression for cos(theta) in terms of itself. To further simplify, you may consider solving it numerically using a graphing calculator or by employing numerical methods. Alternatively, you could rewrite cos(theta) in terms of a different trigonometric function, such as sin(theta), tan(theta), or cot(theta), and then solve for that function instead.