Question

a modulated laser heats a diamond. its variable temperature, in degrees Celsius, is given by f(t)=T sin at. what is the period of the curve?

Answer 1

A general equation for the sine curve is y=a*sin(b*x).
Yours is f(t)=T*sin(a*t).

Since the PERIOD of y=a*sin(b*x) is 2Pi/b,
the PERIOD of y=T*sin(a*t) is 2Pi/a.

Answer 2

That's all you need to do.

Once more: if y=A*sin (Bx), the period of this function is 2Pi/B.

Answer 3

but y r u doin 2pi/a ik tht the formula for period is 2pi/b...

Answer 4

?

Answer 5

I'm sorry, and I do understand why what I typed could be confusing.

Let's start over. If y=A sin Bx, the PERIOD IS 2PI/B.

x is your independent variable, and B is the coefficient of that variable.

Now, you have f(t) = T sin at.

Your independent variable is t. What is the coefficient of t?

Answer 6

a?

Answer 7

Yes, and now the PERIOD of YOUR function is

\[\frac{ 2\pi }{ coefficient.of.a }\]

Answer 8

So, what is the period of YOUR function?

Answer 9

2pi/a