P1 Question

From the old P1 Heinemann book, I cant get my head around this p1 trig question!! I know the question is correct as the answer fits, but for some reason I cant seem to be able to do it! Anybody here know the answer, could they show me the working? Very much appreciated!

4sinxcosx - 2cosx - 2sinx + 1 = 0

Reply 1

Bengaltiger

4sinxcosx - 2sinx - 2cosx + 1 = 0

2sinx( 2cosx - 1 ) - 2cosx + 1 = 0

2sinx( 2cosx - 1 ) - 1( 2cosx -1 ) = 0

( 2cosx - 1 )( 2sinx - 1) = 0

So your 2 equations are
cosx = 0.5
sinx = 0.5

Hope this helps.

Reply 2

badboy killa

Could you please explain how you got from

2sinx( 2cosx - 1 ) - 1( 2cosx -1 ) = 0

to

( 2cosx - 1 )( 2sinx - 1) = 0

Cheers!! I havent done maths in over 2 years, it obviously shows :frown:

bump

Hello!

Say you have to solve the equation
4xy-2y-2x+1=0
2y is a factor of 4xy and of 2y,
and 4xy-2y=2y(2x-1).
So
4xy-2y-2x+1 = 2y(2x-1) -2x+1

Now -2x+1 = -1(2x-1)
so
4xy-2y-2x+1 = 2y(2x-1) -1(2x-1)

Both 2y(2x-1) and -1(2x-1) contain a factor of (2x-1)
so 2y(2x-1) -1(2x-1) = (2x-1) (2y -1)
(because (2x-1)(2y-1) = 2x(2y-1) -1(2y-1)

It works in a similar way with the trig function...
4sinxcosx - 2cosx - 2sinx +1 = 0
2cosx(2sinx - 1) - 2sinx + 1 = 0
as 4sinxcosx and 2cosx both contain a factor of cosx
2cosx(2sinx - 1) -1(2sinx - 1)=0
(2sinx -1) (2cosx -1)=0
because both 2cosx(2sinx -1) and -1(2sinx -1)
both contain the factor 2sinx-1

so 2sinx = 1, so sinx =0.5,
hence x=30, 180-30
x=30, 150

or 2cosx -1 =0, so cos x =0.5
so x=60, 360-60
x=60, 300

and so x=30, 60, 150, 300

love danniella

Reply 5

generalebriety

Explained in more loose terms,

let blah = 2cosx - 1

2sinx( 2cosx - 1 ) - 1( 2cosx -1 ) = 0
2sinx(blah) - 1(blah) = 0

You have 2sinx of them, and you take away 1 of them. How many do you have? 2sinx, minus 1.

(2sinx - 1)(blah) = 0.

but blah = 2cosx - 1.

(2sinx - 1)(2cosx - 1) = 0.