# Math Help - Graphing the trig function from to given points?

1. ## 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

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

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

4. 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...

5. 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!

6. 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?

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

Now what's the next step in the problem

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

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

-4 = a (.7071067812) I think?

10. 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 $\displaystyle a$.

11. 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 $\displaystyle \sin{\frac{3\pi}{4}} = \frac{1}{\sqrt{2}}$.

12. 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 $\displaystyle \sin{45^{\circ}} = \frac{1}{\sqrt{2}}$.

13. 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?

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

15. 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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