Could really use some help

**mazdatuner** · April 11th 2006, 10:05 AM

Im at a point in my book where I have to graph functions of sine and cosine
one such example of the problems is

Graph 1 cycle and lable 5 points on each.
F(x)=sin pie x <---- that is "F of X with sine...then the symbol for pie and x next to it

I know the points and can lable the amplitude and period and I can even graph it on my TI-83 but I am lost when It comes to graphing it by hand ....any help would be great

another question is
Solve for all angles over the interval [0,2pie] such that Sin of theta = 1/2

I have some Ideas and have read the book but I still dont know where to even start with this one either

**ThePerfectHacker** · April 11th 2006, 02:04 PM

Originally Posted by mazdatuner

Im at a point in my book where I have to graph functions of sine and cosine
one such example of the problems is

Graph 1 cycle and lable 5 points on each.
F(x)=sin pie x <---- that is "F of X with sine...then the symbol for pie and x next to it

I know the points and can lable the amplitude and period and I can even graph it on my TI-83 but I am lost when It comes to graphing it by hand ....any help would be great

Try doing this, you need to graph $f(x)=\sin (\pi x)$ .
You know you amplitude it 1 and your period is $\frac{2\pi}{|\pi|}=2$ . On this interval $[0,2]$ you midpoint is a zero, meaning $x=1$ then, $f(x)=0$ . And the mipoints of those, (the quarters of $[0,2]$ ) are the max and min (with amplitude 1), thus at $x=1/2$ and $x=3/2$ you have a max and min resprectively. Then, you can draw a responable graph knowing this.

**ThePerfectHacker** · April 11th 2006, 02:07 PM

Originally Posted by mazdatuner

Solve for all angles over the interval [0,2pie] such that Sin of theta = 1/2

First you know that $\sin (\pi/6)=1/2$ .
But, you still need other solutions on interval $[0,2\pi]$ .
Remember that in the 2nd quadrant the sine is positive. Thus, the other solution appears in the second quadrant. Which is $\pi-\pi/6=\frac{5\pi}{6}$ .
Hence, the two solutions are,
$\theta=\left\{\begin{array}{c}\pi/6\\ 5\pi/6$

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Could really use some help