You are Here: Home >< Maths

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

1. 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
2. Try converting the cos2 x term into a sin2 x term then treating it as a quadratic
3. 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 -.-
4. Yeah that looks good, now you can factorise that and solve for x
5. Sweet, my free just finished so i'll try it when i'm home x
6. 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).
7. why does the sin^2 get ignored I don;t understand
8. (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

or

y = sin(x),

therefore, or

sin-1 () = 30

sin-1 (-3) = Maths error.

0 < x < 2 pi

x = 30, 150 degrees

2 pi = 360 degrees

pi = 180 degrees

= 30 degrees

= 150 degrees.

Hence, x = and
9. (Original post by thegodofgod)
(2y-1)(y+3) = 0

or
Clearly not one of god's better days.
10. Please don't post full solutions
11. (Original post by ghostwalker)
Clearly not one of god's better days.
woops
12. (Original post by EierVonSatan)
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?

On top of that, I'm new to using LaTeX, so I like to practise using it whenever I can
13. (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?

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

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: May 5, 2011
The home of Results and Clearing

### 1,096

people online now

### 1,567,000

students helped last year
Today on TSR

### Took GCSEs this summer?

Fill in our short survey for Amazon vouchers!

### University open days

1. University of Buckingham
Thu, 23 Aug '18
2. University of Glasgow
Tue, 28 Aug '18
3. University of Aberdeen
Tue, 28 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams