Question

Find all solutions in interval (0,2pi)

2 sin^2 (x) + cos (x) = 1

Write in terms of pi


PLEASE HELP!

Answer 1

the answer has to be in radians (in terms of pi)

Answer 2

hi guys! Please help! I will truly appreciate it!

Answer 3

180 degrees

Answer 4

? is that it?

Answer 5

Yes.

Answer 6

how? in terms of pi?

Answer 7

2 sin^2 x - cos x = 1

2(1-cos^2 x) - cos x = 1 where 1=sin^2x + cos^2x

2 - 2cos ^2x - cos x = 1 expand and collect like terms

-2cos^2x - cos x = -1

2cos^2 x + cos x = 1 multiply by negative one (both sides)

2 cos^2 x + cos x - 1 = 0 quadratic equation

You can refer to 'PIANOs' excellent method below, which works with the radical, and always yields an exact answer.

You could have also factored this one:
(2u - 1)(u+1)= 0 could have been used where u = cosx

cosx = 1/2
cosx= -1

So, the 'angles' that jive with that cosine ratio are:

cos x = 1/2
cos^-1 (cosx) = cos^-1 (1/2)
x=60 degrees, or 300 degrees

cosx = -1
cos^-1(cosx) = cos^-1(-1)

x = 180 degrees.

Answer 8

so is the solution just 180 or is there more? and 180 in terms of radian/pi is just pi right?

Answer 9

The question asked for 2 sin^2 x + cos x = 1, not 2 sin^2 x - cos x = 1

Answer 10

yeah
its + not subtraction!

Answer 11

can u help me rich_m_c

Answer 12

Check out this plot and try to tell me the solutions: http://www.wolframalpha.com/input/?i=2sin%5E2%28x%29%2Bcos%28x%29%3D1+from+0+to+2*pi

Answer 13

what?

Answer 14

i dont understsand it

Answer 15

The curve is y=2 sin^2 (x) + cos (x) and where the red line crosses at the red points is y=1

Answer 16

please i am so desperate!

Answer 17

but how do i put the solutions in terms of pi?

Answer 18

Pleasee!

Answer 19

The graph was just an aid to the eye. To find the solution you have to follow a similar method to Drakula's