Find Eqn for sine fcn w/ amplitude 1/2, period 3pi/2, and...

[Jaskaran]

Hello, everyone, I'm deeply boggled on this one (not that much, but the book doesn't offer an example as to how)

Find the equation for the sine of a function, given that amplitude is 1/2, the period is 3pi/2, and phase shift is -pi/4

So do I convert them to degrees or write it in radians? If so, how do I write the equation in radians?

 

[tkhunny]

Try to recall that "radians" isn't really a unit. It is a device for people who have to have units or their heads will explode. Radians are numbers. \(\displaystyle \pi\) is a number. \frac{\pi}{6} is a number. Do NOT convert stuff to degrees unless you have to.

Work one piece at a time.

\(\displaystyle y = \sin(x)\)

Amplitude: 1
Period: \(\displaystyle 2\pi\)
Phase Shift: 0

\(\displaystyle y = \frac{1}{2}\sin(x)\)

Amplitude: 1/2
Period: \(\displaystyle 2\pi\)
Phase Shift: 0

\(\displaystyle y = \frac{1}{2}\sin(\frac{4}{3}x)\)

Amplitude: 1/2
Period: \(\displaystyle (3/2)\pi\)
Phase Shift: 0

\(\displaystyle y = \frac{1}{2}\sin(\frac{4}{3}(x - ?????))\)

Amplitude: 1/2
Period: \(\displaystyle (3/2)\pi\)
Phase Shift: -pi/4

You do the last one.