Are complete cycles in trigonometry always 360 degrees?

[Inertialforce]

Homework Statement

When dealing with periods and amplitudes in trigonometry, are all complete cycles (for cosine, sine, and tan functions) considered to be 360(degrees)?

I'm just wondering, because I want to make sure now so that I can apply it to the appropriate questions when the time comes.

Homework Equations

The Attempt at a Solution

 

[Дьявол]

I think this is the right thing for you: http://catcode.com/trig/trig09.html

Also the period of the trigonometric functions is not same for all of them.

sin(x) and cos(x) have 2k$\pi$ period and tg(x) and ctg(x) have k$\pi$ period.

So if you have:
sinx=a:
$$x=\begin{bmatrix} arcsin(a)+2k\pi\\ \pi - arcsin(a)+2k\pi \end{bmatrix}$$
cosx=a:
$$x=\begin{bmatrix} \pm arccos(a)+2k\pi \\ \end{bmatrix}$$
tgx=a:
$$x=\begin{bmatrix} arctg(a) + k\pi \\ \end{bmatrix}$$
ctgx=a
$$x=\begin{bmatrix} arcctg(a) + k\pi \\ \end{bmatrix}$$

I hope this helped you.

 

[Architeuthis Dux]

In trigonometry, a complete cycle is defined as one full revolution around the unit circle, which is equivalent to 360 degrees or 2π radians. This applies to all trigonometric functions, including cosine, sine, and tangent. Therefore, when dealing with periods and amplitudes in trigonometry, it is safe to assume that one complete cycle is equal to 360 degrees. However, it is important to note that sometimes, problems may involve angles greater than 360 degrees, in which case the concept of periodicity can be applied to find the equivalent angle within one complete cycle. It is always best to clarify with your instructor or refer to the specific problem for any variations in the unit of measurement.