Graphing the trig function from to given points?

**Smokinoakum** · March 18th 2011, 06:47 PM

Hi all...I'm a bit confused about my new Math chapter. In this chapter we start to graph the trigonometry functions. I'm a bit stumped with that alone. Unfortunatly it's an online math class and I have no real outlet to ask any questions.

Anyway...
I have a problem that states.

"Find and graph the function of the form y = a sin x that passes through (3pi/2 , -4)"

I have no idea on how to even start.

Could someone give me some pointers on how this is worked out? Maybe even some calculator tips!

Thanks for your help.

Neil

**Prove It** · March 18th 2011, 06:48 PM

Substitute $\displaystyle (x, y) = \left(\frac{3\pi}{2}, -4\right)$ into $\displaystyle y=a\sin{x}$ and solve for $\displaystyle a$ .

**Smokinoakum** · March 18th 2011, 06:50 PM

Can you give an example? How do you solve for a?

**Prove It** · March 18th 2011, 07:04 PM

Like I said, substitute $\displaystyle x = \frac{3\pi}{4}$ and $\displaystyle y = -4$ into the equation $\displaystyle y = a\sin{x}$ .

Surely you can go from there...

**Smokinoakum** · March 18th 2011, 07:11 PM

Originally Posted by Prove It

Like I said, substitute $\displaystyle x = \frac{3\pi}{4}$ and $\displaystyle y = -4$ into the equation $\displaystyle y = a\sin{x}$ .

Surely you can go from there...

Well I've never done this before, so I just need one problem worked out for me. I have about ten questions just like this and my "online teacher" does not answer emails or show any work!

I'm sure you have better thing to do than run through the basics, but that where I'm at.

I'm Sorry!

**Prove It** · March 18th 2011, 07:14 PM

Where you see $\displaystyle x$ in the equation $\displaystyle y = a\sin{x}$ , replace it with $\displaystyle \frac{3\pi}{4}$ .

Where you see $\displaystyle y$ in the equation $\displaystyle y = a\sin{x}$ , replace it with $\displaystyle -4$ .

What do you get?

**Smokinoakum** · March 18th 2011, 07:16 PM

You get (-4 = a sin 3pi/4) Right?

Now what's the next step in the problem

**Prove It** · March 18th 2011, 07:52 PM

What does $\displaystyle \sin{\frac{3\pi}{4}}$ equal?

**Smokinoakum** · March 18th 2011, 07:59 PM

Originally Posted by Prove It

What does $\displaystyle \sin{\frac{3\pi}{4}}$ equal?

It equals

-4 = a (.7071067812) I think?

**Prove It** · March 18th 2011, 08:02 PM

You should know the exact value of $\displaystyle \sin{\frac{3\pi}{4}} = \frac{1}{\sqrt{2}}$ .

So $\displaystyle -4 = \frac{a}{\sqrt{2}}$ .

Solve for $\displaystyle a$ .

**Smokinoakum** · March 18th 2011, 08:11 PM

Originally Posted by Prove It

You should know the exact value of $\displaystyle \sin{\frac{3\pi}{4}} = \frac{1}{\sqrt{2}}$ .

So $\displaystyle -4 = \frac{a}{\sqrt{2}}$ .

Solve for $\displaystyle a$ .

I came out with -5.656854249 (is this right?)

How did you find $\displaystyle \sin{\frac{3\pi}{4}} = \frac{1}{\sqrt{2}}$ .

**Prove It** · March 18th 2011, 09:03 PM

Sine is positive in the first and second quadrants. An angle of $\displaystyle \frac{3\pi}{4}$ is the same as an angle of $\displaystyle \frac{\pi}{4}$ in the second quadrant. $\displaystyle \frac{\pi}{4} = 45^{\circ}$ .

Draw a $\displaystyle 45^{\circ}, 45^{\circ}, 90^{\circ}$ right-angle triangle of side lengths $\displaystyle 1, 1, \sqrt{2}$ . You should be able to see why $\displaystyle \sin{45^{\circ}} = \frac{1}{\sqrt{2}}$ .

**Smokinoakum** · March 18th 2011, 09:31 PM

Originally Posted by Prove It

Sine is positive in the first and second quadrants. An angle of $\displaystyle \frac{3\pi}{4}$ is the same as an angle of $\displaystyle \frac{\pi}{4}$ in the second quadrant. $\displaystyle \frac{\pi}{4} = 45^{\circ}$ .

Draw a $\displaystyle 45^{\circ}, 45^{\circ}, 90^{\circ}$ right-angle triangle of side lengths $\displaystyle 1, 1, \sqrt{2}$ . You should be able to see why $\displaystyle \sin{45^{\circ}} = \frac{1}{\sqrt{2}}$ .

Thanks for that explanation.

So does a = -5.656854249? or is there another step?

**Prove It** · March 18th 2011, 09:52 PM

Keep $\displaystyle a$ in its exact form...

**Smokinoakum** · March 18th 2011, 09:54 PM

Originally Posted by Prove It

Keep $\displaystyle a$ in its exact form...

Wow...I really feel dumb here. What is a's exact form? LOL

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