Posted by Rivan on Saturday, April 21, 2012 at 2:08am.
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
Related Questions
Precal - I got this far, but now I'm stuck...please help 6cos^2theta - 5cos(...
Calculus - I wanted to confirm that I solved these problems correctly (we had to...
Algebra II - Multiple Choice Which expression is NOT equivalent to 1? (theta) ...
trig - If cosecant of theta equals 3 and cosine of theta is less than zero, find...
help help helpppp--math - 1)Use the definitions sin0(theta) = y/r, cos0(theta...
Math - 1)Use the definitions sin0(theta) = y/r, cos0(theta) = x/r and/or tan0(...
math (trig) - if cos 2 theta = -(1/3) and theta is in Quadrant 2, find sin theta...
Trig - Solve the following interval 0<_ (less than or equal to)0(Theta)&...
Precalculus(NEED HELP ASAP PLEASE!!) - cot(theta)= 3 pi < theta < ...
Algebra II - Which of the following expressions are not equal to 1? A) sin^2 ...
For Further Reading
