Im gonna type some of this in a program called LaTeX. Im not sure if TSR supports this so if it doesnt come out like algebra please just google for a LaTeX translator and copy and paste
Generally y=a+bsin(cx)is a transformation of
Unparseable latex formula:
f(x)=\sin(x)$
So normally you have a typical sine wave (google if you need to, but key points are amplitude = 1 and it hits at the origin and every pi / 2) but then you do something to it. Adding a to the ENTIRE function (i.e. a+f(x)=a+sin(x)then you make the y value at every point 'a' greater - you move the graph vertically upwards or downwards. Now for b instead of adding you're now multiplying the entire function (i.e. bf(x)=bsin(x)) so for every y value you get you multiply it by b. Now this is gonna have a larger effect the larger y is so its not just a translation (moving the graph) its a stretch! Finally onto c. This one was always a bugger to think about but you get used to it and the more you do it the less of a pain it becomes. Now if we multiply every value of x by some constant, c, then what you are doing is changing the input to the function. You're saying 'take the value that would have been at cx and place it at x'. Now again the larger x is the bigger the effect is so you squash the graph! Now have another go at the questions?
I have done that and managed to do i but it took me long How would you go about it? Also am not sure what to do with ii
What is the Range of values for sin (x) ? Clearly -1 < y < 1
In the question in part (i): What are their range of value? (Clearly -3 < y < 3) If they're not the same, what translation/stretch could you do to the sin(x) graph to get their graph?
What is the Range of values for sin (x) ? Clearly -1 < y < 1
In the question in part (i): What are their range of value? (Clearly -3 < y < 3) If they're not the same, what translation/stretch could you do to the sin(x) graph to get their graph?
Hope this helps.
Do a similar thing for ii)
For part (i) the graph is also squashed by scale factor 2 in the x direction. I have figured out i but am struggling with ii still
Im gonna type some of this in a program called LaTeX. Im not sure if TSR supports this so if it doesnt come out like algebra please just google for a LaTeX translator and copy and paste
Generally $y=a+b\sin(cx)$ is a transformation of $f(x)=\sin(x)$. So normally you have a typical sine wave (google if you need to, but key points are amplitude = 1 and it hits at the origin and every $\pi / 2$) but then you do something to it. Adding a to the ENTIRE function (i.e. $a+f(x)=a+\sin(x)$ then you make the y value at every point 'a' greater - you move the graph vertically upwards or downwards. Now for b instead of adding you're now multiplying the entire function (i.e. $bf(x)=bsin(x)$) so for every y value you get you multiply it by b. Now this is gonna have a larger effect the larger y is so its not just a translation (moving the graph) its a stretch! Finally onto c. This one was always a bugger to think about but you get used to it and the more you do it the less of a pain it becomes. Now if we multiply every value of x by some constant, c, then what you are doing is changing the input to the function. You're saying 'take the value that would have been at cx and place it at x'. Now again the larger x is the bigger the effect is so you squash the graph! Now have another go at the questions?
Thanks but the latex thingy isn't working - i tried putting it into the latex software thing but my laptop froze after doing that Apparently there are too many characters
Thanks but the latex thingy isn't working - i tried putting it into the latex software thing but my laptop froze after doing that Apparently there are too many characters
Im gonna type some of this in a program called LaTeX. Im not sure if TSR supports this so if it doesnt come out like algebra please just google for a LaTeX translator and copy and paste
Generally $y=a+b\sin(cx)$ is a transformation of $f(x)=\sin(x)$. So normally you have a typical sine wave (google if you need to, but key points are amplitude = 1 and it hits at the origin and every $\pi / 2$) but then you do something to it. Adding a to the ENTIRE function (i.e. $a+f(x)=a+\sin(x)$ then you make the y value at every point 'a' greater - you move the graph vertically upwards or downwards. Now for b instead of adding you're now multiplying the entire function (i.e. $bf(x)=bsin(x)$) so for every y value you get you multiply it by b. Now this is gonna have a larger effect the larger y is so its not just a translation (moving the graph) its a stretch! Finally onto c. This one was always a bugger to think about but you get used to it and the more you do it the less of a pain it becomes. Now if we multiply every value of x by some constant, c, then what you are doing is changing the input to the function. You're saying 'take the value that would have been at cx and place it at x'. Now again the larger x is the bigger the effect is so you squash the graph! Now have another go at the questions?
You can clearly see that the second time it crosses the x-axis is pi when it's meant to be 2pi therefore it's been stretched by 1/2 which makes it y=3sin2x
Sorry for not spotting this earlier. The perks of using TSR this late
You can clearly see that the second time it crosses the x-axis is pi when it's meant to be 2pi therefore it's been stretched by 1/2 which makes it y=3sin2x
Sorry for not spotting this earlier. The perks of using TSR this late
No worries and thanks but i am not stuck on this - I am stuck on part ii
Notice how at 90 degrees, y=0 but sin(90) is normally equal to y=1. The Normal range for a sin(x) graph is -1<y<1 but now it's 0 < y < 2 this indicates a translation.
There's also a translation of some units in the x-direction, We know this because sin (90) [The tops of the sin graph] normally equals 1, but instead now they appear to have shifted to the right some units; this indicates a translation.
Combine all this information to obtain a solution.
I don't think there's any stretches. Apply the x-translation first before the y-translation.
Notice how at 90 degrees, y=0 but sin(90) is normally equal to y=1. The Normal range for a sin(x) graph is -1<y<1 but now it's 0 < y < 2 this indicates a translation.
There's also a translation of some units in the x-direction, We know this because sin (90) [The tops of the sin graph] normally equals 1, but instead now they appear to have shifted to the right some units; this indicates a translation.
Translation of what units in the x direction? That's what im mostly confused with
Red graph is y = sin(x) Blue graph is y = sin (-x) Green Graph is y = sin (-x) 1
btw a translation of (x - 90 degrees) or (x 90 degrees) is always equal to the reflection of the graph in the y-axis PROVIDED IT IS A Trigonometric graph.