SOLUTION: find all values of feta, to the nearest degree, that satisfy the equation 7cos cubed feta=5cos squared feta+cos feta in the interval 0 degrees to 360 degrees

Question 723880: find all values of feta, to the nearest degree, that satisfy the equation 7cos cubed feta=5cos squared feta+cos feta in the interval 0 degrees to 360 degrees
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
-->
So that I do not have to keep writing so many times, I will define a shorter-named variable

Using the newly defined variable I can write the equation as

That is much easier to type.
Now, we solve for x:
--> (taking out as common factor)
The solutions are and the solutions to the quadratic equation
, which we can find by using the quadratic formula:

The two values we get from the quadratic formula are approximately
and (rounding)
corresponds to and for in the interval between and , because those are the only two angles with zero cosine in that interval.
From we get (rounded) and
(also a rounded approximation).
From we get (rounded) and
(also a rounded approximation).
RELATED QUESTIONS
let (7, -5) be a point on the terminal side of feta. find the exact values of cos feta,... (answered by lwsshak3)

Find all values of θ, to the nearest degree, that satisfy the equation 7cos... (answered by lwsshak3)

graph y=sin feta and y=sin ( negative feta) generate two equations for y+sin(negative (answered by richard1234)

If cos(feta)=0.7 find exact values for tan(feta) and sin(feta) (answered by tommyt3rd)

if csc (feta) = -5/3 and (feta) has its terminal side in Quadrant 3, find the exact value (answered by oscargut)

Find csc feta if sin feta = the square root of 5 divided by... (answered by Fombitz)

Given that cos(feta)=a/b, what is the vale of feta (circle with line through it) Right (answered by stanbon)

Hi, my math book says that cos (-feta) = +cos feta How is this... (answered by jsmallt9)

7cos theta + 1 = 6sec theta Find, to the nearest degree, all values of theta in the... (answered by lwsshak3)