Question

Solve the given equation in the interval [0,2 pi].
Note: The answer must be written as a multiple of pi. Give exact
answers. Do not use decimal numbers. The answer must
an integer or a fraction. Note that pi is already provided with the
answer so you just have to find the appropriate multiple. E.g.
the answer is p/2 you should enter 1/2. If there is more than one
answer write them separated by commas.
2(sin(x))^2−5cos(x)+1 = 0
x=__________ pi

Answer 1

2(sin(x))^2−5cos(x)+1 = 0
2(1- cos^2(x))−5cos(x)+1 = 0
2 - 2cos^2(x) - 5cos(x) + 1 = 0
2cos^2(x) + 5cos(x) + 3 = 0

(cosx + 1 )(2cosx + 3) = 0
cosx = -1 or cosx = -3/2

from the first part x = 0 or 2pi
there is no solution to the second part since the cosine function cannot exceed ±1

Answer 2

Thats not correct....
I'm not sure how you got from
2 - 2cos^2(x) - 5cos(x) + 1 = 0
2cos^2(x) + 5cos(x) + 3 = 0
It should be -2cos^2(x) - 5cos(x)+1=0

From there I'm stuck.

Answer 3

sorry. meant
-2cos^2(x) - 5cos(x)+3=0

Answer 4

Thanks for catching my error,
of course if cos x = -1 then x = pi.

I read my own writing as cosx = 1, (let's blame it on eyesight of an old guy, lol)

you said:"I'm not sure how you got from
2 - 2cos^2(x) - 5cos(x) + 1 = 0 "

look at 2(1- cos^2(x)) and expand it, you get
2 - 2cos^x

so x = pi is your only solution

Answer 5

Oh my, OH my, two errors in the same post, I must be getting careless.

Let's start from

2(1- cos^2(x))−5cos(x)+1 = 0
2 - 2cos^2(x) - 5cos(x) + 1 = 0
2cos^2(x) + 5cos(x) - 3 = 0
(cosx + 3)(2cosx - 1) = 0
cosx = -3 which will not produce an answer
or
cosx = 1/2
so x = pi/3 or 5pi/3 (60º or 300º)

(these answers are correct, I tested them)

Answer 6

Thank you....the pi/3, 5pi/3 is correct.