trig wave equations

**killer786** · Jan 18th 2010, 06:58 AM

well im having quite alot of trouble doing questions like these could someone give me some insight into how they should be done thank you!

A function f(x) is known to be of the form F(x)=Acos(px+q) + B. It has a local maximum at (6, 8) and the next local minimum is at (10, 2). Find the constants A, p, q and B and hence give the formula for the function.

**Grandad** · Jan 18th 2010, 07:20 AM

Hello killer786

Welcome to Math Help Forum!

Originally Posted by killer786

well im having quite alot of trouble doing questions like these could someone give me some insight into how they should be done thank you!

A function f(x) is known to be of the form F(x)=Acos(px+q) + B. It has a local maximum at (6, 8) and the next local minimum is at (10, 2). Find the constants A, p, q and B and hence give the formula for the function.

The function $\cos(px+q)$ has a maximum value $+1$ when $px +q = 0, 2\pi, 4\pi, ...$ and a minimum value $-1$ when $px+q = \pi, 3\pi, 5\pi, ...$ Since there are multiple maxima and minima, there will be multiple values of $p$ and $q$ . Below, I've taken the first (and most obvious) values.

So $f(x)$ varies between $B+A$ and $B-A$ . Since these maximum and minimum values are 8 and 2 respectively, we get: