# Thread: Graphing the trig function from to given points?

1. Leave the answer in radical form unless told otherwise. It is easier to write and remember.

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

How do you undo dividing by $\displaystyle \displaystyle \sqrt{2}$?

3. Originally Posted by Prove It
$\displaystyle \displaystyle -4 = \frac{a}{\sqrt{2}}$.

How do you undo dividing by $\displaystyle \displaystyle \sqrt{2}$?
I guess I'm more of a visual learner, which is why I need to see the full problem worked out, study the process, understand the logic, and then apply what I learn.

So (a = 4)

I still would like to see the whole problem worked out for my notes. I still confused.

4. note that $\displaystyle a \ne 4$

$\displaystyle -4 = \dfrac{a}{\sqrt{2}}$

to solve for $\displaystyle a$ , multiply both sides by $\displaystyle \sqrt{2}$ ...

$\displaystyle a = -4\sqrt{2}$

also, your instructor should have introduced you to the exact trig values of sine and cosine on the unit circle. (then you would have known the exact value of $\displaystyle \sin\left(\frac{3\pi}{4}\right)$ w/o consulting your calculator)

5. Originally Posted by skeeter
note that $\displaystyle a \ne 4$

$\displaystyle -4 = \dfrac{a}{\sqrt{2}}$

to solve for $\displaystyle a$ , multiply both sides by $\displaystyle \sqrt{2}$ ...

$\displaystyle a = -4\sqrt{2}$

also, your instructor should have introduced you to the exact trig values of sine and cosine on the unit circle. (then you would have known the exact value of $\displaystyle \sin\left(\frac{3\pi}{4}\right)$ w/o consulting your calculator)

Very cool! That helps a lot.

Well I entered in $\displaystyle a = -4\sqrt{2}$ in my assignment and it said that it was wrong?

The answer was (the function y = ( 4 ) sin x passes through (3pi/2 , -4)

I think I've confused both myself and you generous people helping me out. Such is learning this stuff online and not in a class room.

What have I missed here?

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

Surely you can go from there...
This is where some of the confusion happened!

He should have said "substitute $\displaystyle \displaystyle x = \frac{3\pi}{2}$ and $\displaystyle \displaystyle y = -4$ into the equation"

Not "substitute $\displaystyle \displaystyle x = \frac{3\pi}{4}$ and $\displaystyle \displaystyle y = -4$ into the equation"

So the equation should be $\displaystyle \displaystyle -4 = a\ sin \frac{3\pi}{2}$ right?

7. OK...going from what Prove It helped me out with, this is what I have figured out.

Find the function of the form $\displaystyle \displaystyle y = a\ sin\ x$ that passes through $\displaystyle \displaystyle \left(\frac{3\pi}{2}, -4\right)$

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

$\displaystyle \displaystyle -4 = a\ sin \frac{3\pi}{2}$

$\displaystyle \displaystyle sin \frac{3\pi}{2} =\ -1$

$\displaystyle \displaystyle -4 =\frac{a}{-1}$

$\displaystyle \displaystyle -4 (-1) =\ 4$

$\displaystyle \displaystyle a =\ 4$

8. Originally Posted by Smokinoakum
OK...going from what Prove It helped me out with, this is what I have figured out.

Find the function of the form $\displaystyle \displaystyle y = a\ sin\ x$ that passes through $\displaystyle \displaystyle \left(\frac{3\pi}{2}, -4\right)$

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

$\displaystyle \displaystyle -4 = a\ sin \frac{3\pi}{2}$

$\displaystyle \displaystyle sin \frac{3\pi}{2} =\ -1$

$\displaystyle \displaystyle -4 =\frac{a}{-1}$

$\displaystyle \displaystyle -4 (-1) =\ 4$

$\displaystyle \displaystyle a =\ 4$

Sorry about the confusion before, thought it said $\displaystyle \displaystyle x = \frac{3\pi}{4}$.
Yes, you have now correctly found $\displaystyle \displaystyle a$.
So the equation of your function is $\displaystyle \displaystyle y = 4\sin{x}$. This is the same as the function $\displaystyle \displaystyle \sin{x}$, being stretched by a factor of $\displaystyle \displaystyle 4$ vertically.