Hello.
I have just encountered this problem. I want to find a cosine function with the graph represented on the picture below.
I have found the following:
But I am unable to find . So then my question would be: How do I find it, please?
In advance, thank you for spending time and efforts on my problems :]
Thank you for your reply, flyingsquirrel.
The task doesn't say anything about however, the correct answer should be that
I am not sure how you found , so please feel free to elaborate on that. :]
Furthermore, I didn't understand how you found that:
(What I mean is, how do you know it is equal to two?)
I don't know if you made a typo or misread but . I chose this value because the link between and is simple hence once you know you can easily find . I've no other jusification, I just noted this.
Furthermore, I didn't understand how you found that:
(What I mean is, how do you know it is equal to two?)
@ flyingsquirrel
Oh, yes, sorry about that typo, hehe. Thank you for the explanation, it is much more clear now. If you have other methods, please feel free to educate me on those too. :]
Again, thank you very much for your time and help, I appreciate it!
Another method would be using inverse trigonometric functions.
(we still work with )
Using the graph, we know that (y-intercept) hence . This gives us two values for : either either . To determine which of the two values is the right one, let's use another point. For example, we know that (x-intercept for ) hence has to satisfy the equation which is only possible if .
@ flyingsquirrel
Thank you very much for the other method. :]
If you still have some time, I'd like to go back to the thing. I am sorry if I come across as thick, but as you have probably noted from my signature, I have some issues regarding terminology etc.
The problem is that I don't understand how you found to beOriginally Posted by flyingsqurirrel
Is this because it would cancel out the period for the function and then set it to zero? Let me give you an example of what I mean.
If
would: which gives us:
So then, when we know that and ?
If so, how do you know that ?
Sorry about the lengthy and messy post, but I can't help being curious and craving understanding here, hehe.
Yes ! (I should have written this in one of my previous posts...)
OKLet me give you an example of what I mean.
If
would: which gives us:
I'm not sure to understand what you mean. Anyway : the cosine function is -periodic hence without the condition , could be any number . As we only want one value of , we add the condition . This gives us a unique solution : . Note that one can choose any interval as long as its "length" is : we could have set ... (usually one takes in or in )So then, when we know that and ?
If so, how do you know that ?
Then, from the condition we can find the interval in which lies :
We know that
Multiply the inequalities by -1 :
Multiplying by we get
Simplifying, it gives us :
In other words : . (I should also have explained this in one of my previous posts )