Help with curves and identities and whatnot

To be perfectly honest I have no idea what topic this comes under, but anyway here goes:

Show that the curves y = 3sin\theta + 1 and y=2cos²\theta will intersect when

2sin² + 3sin\theta- 1 = 0

I've spent 20 mins trying to work it out but I have no clue what to do. I haven't seen a question like this before...

Reply 1

claret_n_blue

When do two curves intersect? When they both go through the exact same point.

How do you work out the 1 point that two curves go through?

Reply 2

Alleykat606

Original post by claret_n_blue

When do two curves intersect? When they both go through the exact same point.

How do you work out the 1 point that two curves go through?

uhh....simultaneous equation? :colondollar:

Reply 3

claret_n_blue

Original post by Alleykat606

uhh....simultaneous equation? :colondollar:

Yeap

Reply 4

TenOfThem

Original post by Alleykat606

uhh....simultaneous equation? :colondollar:

set them equal to each other

spot that the answer has no cos

Use a well know identity to change your cos to sin

Reply 5

Alleykat606

Original post by claret_n_blue

Yeap

but what does the last equation have to do with it? :confused:

Reply 6

claret_n_blue

Original post by Alleykat606

but what does the last equation have to do with it? :confused:

That's the answer to the question. You are showing the curves intersect at that point. So after your calculations are complete, you should get that answer.

Reply 7

Alleykat606

Original post by claret_n_blue

That's the answer to the question. You are showing the curves intersect at that point. So after your calculations are complete, you should get that answer.