Thread: Circular Functions

Hey Ive got two questions regarding Cicular Functions, could you possibly include some working as I am really struggling with this topic:

I need to find the next four values for (t):
6=3sin(2t)+3
I know the first one is 5(pie)/4, i think the second is 9(pie)/4

and
between (pie) and 4(pie)
y=2sin(3t-(pie)/4)+8 for which y attains the minimum value.

thanks guys
RoboStar

Originally Posted by RoboStar

Hey Ive got two questions regarding Cicular Functions, could you possibly include some working as I am really struggling with this topic:

I need to find the next four values for (t):
6=3sin(2t)+3
I know the first one is 5(pie)/4, i think the second is 9(pie)/4

Yes I think you are right

between (pie) and 4(pie)
y=2sin(3t-(pie)/4)+8 for which y attains the minimum value.

thanks guys
RoboStar

y=2sin(3t-(pie)/4)+8

Minimum value of function is -1. So minimum value of y could be 6.The real question is does there exist a t between (pie) and (4pie), such that this happens.
sin(3t-(pie)/4) = -1 means that

Thus

So

In general

So between an , we have three angles that satisfy:

and the minimum value is

and for the first question, would the next two be 13(pie)/4 and 17(pie)/4? I'm still quite unsure with this concept.

Originally Posted by RoboStar

[snip]
I need to find the next four values for (t):
6=3sin(2t)+3
I know the first one is 5(pie)/4, i think the second is 9(pie)/4

[snip]

Do you need values such that t > 0. If so, you missed t = pi/4

Note that your equation can be re-arranged into sin(2t) = 1.

The general solution is where n is an integer.

So get all the solutions you want by letting n = 0, 1, 2, .... -1, -2, ....

Originally Posted by RoboStar

and for the first question, would the next two be 13(pie)/4 and 17(pie)/4? I'm still quite unsure with this concept.

Yes (they correspond to n = 3 and n = 4).