Question

For the following eqn, what are the step to transform it?

Answer 1

\[\huge y= -\frac{5}{3} \sin \frac{9}{4}(-x+ \frac{3 \pi}{2}) + 3\]

Answer 2

What does the -x do? the -A (-5/3)?

Answer 3

@FoolForMath

Answer 4

what does it do? that 'x' is the variable (ofcourse its a part of the argument of SIN). when the values of x change, the corresponding values of y change too according to the function above ^^.

and I don't see any 'A'

Answer 5

A refers to 5/3

Answer 6

@apoorvk

Answer 7

The negatives... what reflections occur?

Answer 8

okay, that 'A' is limiting the amplitude of the function.

We know a sine function can have a maximum value of 1 and a min. of -1.
Now multiplying the whole function by -5/3 does two things. first it multiplies the amplitude by 5/3. next, the negative sign flips the graph about X-axis.

Answer 9

what does the -x do

Answer 10

@apoorvk

Answer 11

hmm the "-x".
so what is sin(-x)? Its (-sinx). so what it does is that it flips the graph again!!! restoring it to its previous "glory".

multiply that (9/4) into the argument. the argument changes to [(-9/4)x + 27pi/8]

now this 27pi/8 is the initial phase of the system. basically shifts the argument of sine by that amount.

Do one thing, try to find out the sine values of this function for different values of x like, 0, pi/2, pi, 2pi, etc, to see how this function behaves.

Answer 12

\[y={−5\over3}\sin{9\over4}(−x+{3π\over2})+3\]
\[0.059(-x+{3pi\over2})+3\]
\[y-3=0.059(-x+{3pi\over2})\]
\[{y-3\over0.059}=(-x+{3pi\over2})\]
\[{y-3\over0.059}={-3pix\over2}\]
And thats as far as I care to go for now.

Answer 13

If you mean by transform, making x the subject

\[y = -5/3 \sin 9/4(-x +3pi/2) + 3\]

subtract 3 from both sides

\[y-3 = -5/3 \sin 9/4(-x +3pi/2)\]

multiply both sides by - 3/5

\[(-3(y -3))/5 = \sin 9/4(-x +3pi/2)\]

take the inverse or arc sin of both sides

\[sin^{-1}(-3(y -3))/5 = 9/4(-x +3pi/2)\]

multiply both sides by 4/9

\[4/9 sin^{-1}(-3(y -3))/5 = (-x +3pi/2)\]

subtract 3pi/2 from both sides

\[4/9 sin^{-1}(-3(y -3))/5 - 3pi/2 = -x\]

multiply by -1

\[- 4/9 sin^{-1}(-3(y -3))/5 - 3pi/2 = x\]

Answer 14

if you ment find the inverse of the function swap x and y

Answer 15

oops missing a bracket the final answer should be

\[x = -4/9 \sin^{-1} (-3(y - 3)/5) - 3 pi /2\]