0
votes
2answers
17 views

Condition of periodic function for |sin πx|

Period of |sin πx| = 1 Wolfram alpha : So why this condition for Periodic function is not true? f(x) = f(x + T) Wolfram alpha :
4
votes
2answers
342 views

How to show that this real function is not periodic?

How can one prove that $$\cos\left(\frac{\pi}{2} t \right)+\cos\left(t \right)$$ is not periodic? This question is motivated by the harmonic spectral representation of time series. Indeed, it is ...
0
votes
1answer
55 views

Proving the fundamental period of tangent

I'm very new to math and proofs -- so I apologize if my math skills and vocabulary offends you. I have a question that states: Prove that PI is a fundamental period of the tangent function. I need ...
1
vote
1answer
69 views

Finding period of a periodic function

I am having some trouble finding the period of this function: $$W(\omega) = \frac{\sin[(2N +1)\omega \Delta t / 2]}{(2N + 1)\sin[\omega \Delta t /2]}$$ Here $N$ is an integer, $\omega$ is angular ...
1
vote
3answers
162 views

How to prove periodicity of a trigonometric function

$f(x)= \sin(2x)+3\cos(8x)$ Is the function periodic ? What I did is equalize $f(x)=f(x+T)$ and after noting that $\sin(2x)=\sin(2T)=\sin(8x)=0$ and $\cos(2x)=\cos(2T)=\cos(8x)=1$ we get that ...
-2
votes
1answer
123 views

Is this function periodic? [closed]

Is the following function periodic? $$f(x)=\cos(x)*\cos(x\sqrt5)$$ A function $f$ is said to be periodic with period $P$ ($P$ being a nonzero constant) if we have $$f(x+P) = f(x)$$ for all ...
11
votes
2answers
544 views

$\cos(x)+\cos(x\sqrt{2})$ is not periodic

Show that the function $$f(x)=\cos(x)+\cos(x\sqrt{2})$$ is not periodic. I tried $x = a$ and $a\sqrt{2}$. I am guessing that the method of contradiction would be of some help over here. What else ...
0
votes
2answers
276 views

Trigonometric Identities - Assignment

How do I simplify Cos(5 theta)? I got as far as Cos(2theta + 3theta). Do I then say Cos(2theta + 3theta) = Cos(2theta) + Cos(3theta)? In that case, how do I get Cos(3theta)?
3
votes
3answers
1k views

Express $\sin 4\theta$ by formulae involving $\sin$ and $\cos$ and its powers.

I have an assignment question that says "Express $\sin 4\theta$ by formulae involving $\sin$ and $\cos$ and its powers." I'm told that $\sin 2\theta = 2 \sin\theta \cos\theta$ but I don't know how ...
0
votes
2answers
64 views

Find the period of the related function

If F is any function with a period of $6$, determine the period of each related function below: $y = f(x+1)$ $\displaystyle y = f(\frac{x}{2})$ I know that the basic definition of a period is $f(x) ...
2
votes
2answers
102 views

calculate the period of an hypotrochoid

I'm curious how to find out the period of an hypotrochoid. x = (a-b) * cos(t) + h * cos( ((a-b)/b) * t ) y = (a-b) * sin(t) - h * sin( ((a-b)/b) * t ) I know ...
6
votes
3answers
946 views

What is the periodicity of the function $\sin(ax) \cos(bx)$ where $a$ and $b$ are rationals?

So, I have a general question first. What happens to the periodicity when we multiply two periodic trig functions with one another ? The next one is very specific, what is the period of the function ...
0
votes
2answers
37 views

Is it okay to use the same variable to describe function periods?

If I have a system of period functions of $x$ and $y$, in this case trigonometric, $$\begin{cases} \sin{(2x + y)} = 0 \\ \sin{(2y + x)} = 0 \end{cases}$$ is it okay for me to to use the ...
3
votes
4answers
1k views

Are sin and cos the only continuous and infinitely differentiable periodic functions we have?

Sin and cos are everywhere continuous and infinitely differentiable. Those are nice properties to have. They come from the unit circle. It seems there's no other periodic function that is also ...