# Graphing the trig function from to given points?

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• Mar 18th 2011, 07:47 PM
Smokinoakum
Graphing the trig function from to given points?
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!

Neil
• Mar 18th 2011, 07:48 PM
Prove It
Substitute $\displaystyle (x, y) = \left(\frac{3\pi}{2}, -4\right)$ into $\displaystyle y=a\sin{x}$ and solve for $\displaystyle a$.
• Mar 18th 2011, 07:50 PM
Smokinoakum
Can you give an example? How do you solve for a?
• Mar 18th 2011, 08:04 PM
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...
• Mar 18th 2011, 08:11 PM
Smokinoakum
Quote:

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!
• Mar 18th 2011, 08:14 PM
Prove It
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?
• Mar 18th 2011, 08:16 PM
Smokinoakum
You get (-4 = a sin 3pi/4) Right?

Now what's the next step in the problem
• Mar 18th 2011, 08:52 PM
Prove It
What does $\displaystyle \sin{\frac{3\pi}{4}}$ equal?
• Mar 18th 2011, 08:59 PM
Smokinoakum
Quote:

Originally Posted by Prove It
What does $\displaystyle \sin{\frac{3\pi}{4}}$ equal?

It equals

-4 = a (.7071067812) I think?
• Mar 18th 2011, 09:02 PM
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 $\displaystyle a$.
• Mar 18th 2011, 09:11 PM
Smokinoakum
Quote:

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 $\displaystyle \sin{\frac{3\pi}{4}} = \frac{1}{\sqrt{2}}$.
• Mar 18th 2011, 10:03 PM
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 $\displaystyle \sin{45^{\circ}} = \frac{1}{\sqrt{2}}$.
• Mar 18th 2011, 10:31 PM
Smokinoakum
Quote:

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?
• Mar 18th 2011, 10:52 PM
Prove It
Keep $\displaystyle a$ in its exact form...
• Mar 18th 2011, 10:54 PM
Smokinoakum
Quote:

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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