Graphs of trigonomic functions

uberkrissy · #1 $Old$ November 4th, 2009, 11:11 PM

These are problems involving sinusoidal graphs:

$f(x)=-1+4cos\frac{\pi}{3}(x-0.5)$

(a) f(5)
(b) f(x)=1

$f(t)=50+20cos\frac{2\pi}{6}(x-0.5)$

(a) f(t)=50
(b) f(40) -- I'm supposed to identify where the sinusoidal graph has a value of 40 at 4 different points.

VonNemo19 · #2 $Old$ November 6th, 2009, 11:43 PM

Quote:

Originally Posted by uberkrissy $View Post$

These are problems involving sinusoidal graphs:

$f(x)=-1+4cos\frac{\pi}{3}(x-0.5)$

(a) f(5)
(b) f(x)=1

$f(t)=50+20cos\frac{2\pi}{6}(x-0.5)$

(a) f(t)=50
(b) f(40) -- I'm supposed to identify where the sinusoidal graph has a value of 40 at 4 different points.

Did you perform the indicated operations? What are you having trouble with here?

uberkrissy · #3 $Old$ November 9th, 2009, 12:53 AM

I graphed them but I need help finding a and b of each equation.

HallsofIvy · #4 $Old$ November 9th, 2009, 04:33 AM

To find f(5) you just replace "x" with "5" in the formula:
$f(x)=-1+4cos\frac{\pi}{3}(5-0.5)$
That should be easy. You shouldn't even need a calculator.

The second problem asks you to solve an equation: $f(x)=-1+4cos\frac{\pi}{3}(x-0.5)= 1$ so add 1 to both sides: $4cos\frac{\pi}{3}(x-0.5)= 2$ , and then divide both sides by 4: $cos\frac{\pi}{3}(x-0.5)= 1/2$ . Now, for what angles is cosine equal to 1/2?

For $f(t)=50+20cos\frac{2\pi}{6}(x-0.5)= 50$ start by subtracting 50 from both sides of the equation.

I'm not clear on your last question:
"f(40) -- I'm supposed to identify where the sinusoidal graph has a value of 40 at 4 different points."

Are you to evaluate f(40), which has a single value, or are you to find 4 different solutions of f(t)= 40?