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2cos^2(x) + 1 = 5sin(x)

Can someone post a method for working this out?

I havn't finished my core2 course yet but doing a past paper...

Perhaps I am missing some crucial rule or something?

SAFL x
Try converting the cos2 x term into a sin2 x term then treating it as a quadratic :smile:
Reply 2
So...

2(1 - sin^2(x)) + 1 = 5sin(x)

and hence

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

Be correct as a starting point then?

The question wants the solutions between the interval 0 < x < 2pi

I guess i'll have to wait till we cover this more in class -.-
Yeah that looks good, now you can factorise that and solve for x
Reply 4
Sweet, my free just finished so i'll try it when i'm home x
Reply 5
You may find it easier to substitute something like y=sin(x) to make is a bit easier to look at. Then when you have your two values for y, you can make those equal to sin(x).
Reply 6
why does the sin^2 get ignored I don;t understand
Original post by sofiane567
why does the sin^2 get ignored I don;t understand


2cos2(x) + 1 = 5sin(x)

2 [1 - sin2(x)] + 1 = 5sin(x)

2 - 2sin2(x) + 1 = 5sin(x)

2sin2(x) + 5sin(x) - 3 = 0

Let y = sin (x).

2y2 + 5y - 3 = 0

(2y-1)(y+3) = 0

y=12y = \frac{1}{2} or y=3y = -3

y = sin(x),

therefore, sin(x)=12sin (x) = \frac{1}{2} or sin(x)=3sin (x) = -3

sin-1 (12\frac{1}{2}) = 30

sin-1 (-3) = Maths error.

0 < x < 2 pi

x = 30, 150 degrees

Convert 30, 150 into radians.

2 pi = 360 degrees

pi = 180 degrees

pi6\frac{pi}{6} = 30 degrees

5pi6\frac{5 pi}{6} = 150 degrees.

Hence, x = pi6\frac{pi}{6} and 5pi6\frac{5 pi}{6}
(edited 12 years ago)
Original post by thegodofgod

(2y-1)(y+3) = 0

y=12y = \frac{1}{2} or y=0y = 0



Clearly not one of god's better days.
Please don't post full solutions :hmmm:
Original post by ghostwalker
Clearly not one of god's better days.


woops :K:
Original post by EierVonSatan
Please don't post full solutions :hmmm:


But if I post it once, will it not help him (or her) the next time - so he (or she) doesn't have to post again for a similar question? :redface:

On top of that, I'm new to using LaTeX, so I like to practise using it whenever I can :ninja: :getmecoat:
Original post by thegodofgod
But if I post it once, will it not help him (or her) the next time - so he (or she) doesn't have to post again for a similar question? :redface:

On top of that, I'm new to using LaTeX, so I like to practise using it whenever I can :ninja: :getmecoat:


No, it encourages people to put up their homework and get it done for them and they learn little if anything. Guide them to the answer wherever possible :yes:
Reply 13
How u get 150 degrees?
Original post by Hanisz
How u get 150 degrees?

This thread is seven years old. Please start a new thread if you want to ask something.

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