Leave the answer in radical form unless told otherwise. It is easier to write and remember.
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?
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?
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} $
$\displaystyle \displaystyle -4 (-1) =\ 4$
$\displaystyle \displaystyle a =\ 4$
Does this follow the concept?
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.