grade 12 functions help

[hamid14]

We started on graphing trig functions using radians instead of degrees this year. What I don't understand is how to get the 5 key points on the graph, how would I figure out at which x-value will the y be at 1, -1 or 0. My teacher told us in class to take the phase shift and the period / 4 and then find a common denominator and use that as the increment increase value.

for example:

y = - 2 sin (1/3 * (x - 5*PI/6) )

i get the period as 2 * PI / (1/3) as 6*PI. And the graph starts at -5*pi / 6 and ends at 31*pi/6.

So then im looking for the increment value so i can put x-values on the graph and a common denominator between -5*pi/6 and 3*pi/2 (period divided by 4) and got pi / 6.

This is the part where im stuck, i dont understand how to plot the x-values on the graph and how to find the 5 main points on the graph other than the starting point and the end point. If anyone can help me with this, I'd appreciate it.

[crossley7]

Start with graphing the original function then translate the function 1 step at a time.

vertical stretch/reflect
horizontal stretch
horizontal translation

The first and second step are interchangeable and could be done in 1 if you wanted

[Brightguy]

hamid14 @ Sun Sep 18, 2011 9:30 am wrote:

And the graph starts at -5*pi / 6 and ends at 31*pi/6.

Unless you miswrote the function, you are shifting the graph in the wrong direction.

hamid14 @ Sun Sep 18, 2011 9:30 am wrote:

i dont understand how to plot the x-values on the graph and how to find the 5 main points on the graph other than the starting point and the end point.

sin(x) has roots at what you seem to be calling its "starting" and "ending" points, as well as a root precisely between these points. This will be preserved after those affine transformations, so one of the "main points" as you call it will occur precisely between the "starting" and "ending" points. The others occur at the function's maximum and minimum, which will be exactly between the middle and start/end points. In other words, all points are separated by the function's period/4.