Substitute :
cos ( theta ) = u
6 cos ^ 2 ( theta ) + 5 cos ( theta ) = 1
6 u ^ 2 + 5 u = 1
6 u ^ 2 + 5 u - 1 = 0
The exact solutions are :
u = 1 / 6
cos ( theta ) = 1 / 6
theta = cos ^ - 1 ( 1 / 6 )
_________________________________
cos ^ - 1
is the inverse cosine function
__________________________________
and
u = - 1
cos ( theta ) = - 1
theta = pi [ radians ] = 180 °
The cosine function have periode 2 pi n
where nis an integer.
So the solutions are :
theta = 2 pi n + cos ^ - 1 ( 1 / 6 )
theta = 2 pi n - cos ^ - 1 ( 1 / 6 )
and
theta = 2 pi n + pi
theta = 2 pi n - pi
P.S.
If you don't know how to solve equation :
6 u ^ 2 + 5 u - 1 = 0
Then in google type:
quadratic equation online
When you see list of results click on:
Free Online Quadratic Equation Solver:Solve by Quadratic Formula
When page be open in rectangle type:
6 u ^ 2 + 5 u - 1 = 0
and click option: solve it
You will see solution step-by step
6cos^2 theta + 5cos theta=1
Solve for theta
1 answer