# How to find the intersection of this complex graph

Hey guys, I’ve attempted this question multiple times yet I can’t seem to get to the answer.

How do I find the intersect between the equations
y= sinxcos2x and y=1/2 - sin2xcosx

The mark scheme seemed to get the answer sin3x=1/2 and get exact answers.
However I keep getting 4sin^3x -3sinx + 1/2 = 0 which doesn’t allow me to get exact values. I used the double angle formula.
How do I manipulate this equation
Original post by harlz_chalamet
Hey guys, I’ve attempted this question multiple times yet I can’t seem to get to the answer.

How do I find the intersect between the equations
y= sinxcos2x and y=1/2 - sin2xcosx

The mark scheme seemed to get the answer sin3x=1/2 and get exact answers.
However I keep getting 4sin^3x -3sinx + 1/2 = 0 which doesn’t allow me to get exact values. I used the double angle formula.
How do I manipulate this equation

4sin^3(x) -3sin(x) is equivlalent to -sin(3x). For an exact answer you generally want a multiple angle so combine (addition identity) the 2x and x to get 3x rather than splitting the 2x.
(edited 6 months ago)
Original post by mqb2766
4sin^3(x) -3sin(x) is equivlalent to -sin(3x). For an exact answer you generally want a multiple angle so combine (addition identity) the 2x and x to get 3x rather than splitting the 2x.

How did you do that step by step?
I’m a bit confused on how you managed to get 3x
Original post by harlz_chalamet
How did you do that step by step?
I’m a bit confused on how you managed to get 3x

The 4sin^3(x) -3sin(x) = -sin(3x) is just the triple angle identity, but they wouldnt have expected you to spot that, rather theyd expect you to use the addition identity as when you equate ys and take the trig terms to one side then
sin(3x) = sin(2x+x) = sin(x)cos(2x) + sin(2x)cos(x)
(edited 6 months ago)