Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Getting tired.

For the curve y = cos (px - q)°, where p and q are positive constants and q<180. The curve cuts the x-axis at points A, B and C.

Given that the coordinates of A and B are (100,0) and (220,0) respectively:

i) write down the coordinates of C
ii) Find the value of p and the value of q

I get the coordinates of C as (340,0), which is the answer in my book.
For p I get 1.5, which is also the answer in my book. But for q I get 40, whereas the book gives 60.

Last edited by Daniel123 (2007-10-23 23:59:27)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Getting tired.

Easy enough to check.

You're given that y crosses the x-axis at x=100.
You know that f = cos(1.5x - q), so therefore 0 = cos(150-q).
cos90 = cos(150-q)
∴ q=60.

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Why did the vector cross the road?
It wanted to be normal.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Getting tired.

Thanks.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Getting tired.

The curve cuts the x-axis at infinitely many points. How do we know which three points A, B and C are?

All right, let’s assume that A, B and C are three consecutive points at which the curve cuts the x-axis. Then C could be 340, but C could also be −20, with the same values for p and q as before. Indeed, C could even be between A and B, in which case C = 160, p = 3 and q = 30.

Last edited by JaneFairfax (2007-10-23 23:40:02)