# Circular Functions of Real Numbers

Graphing the Trigonometric Functions
7:47 — by patrickJMT

Tip: This isn't the place to ask a question because the teacher can't reply.

## Key Questions

• This key question hasn't been answered yet.
• Her are the graphs of the six trigonometric functions.

$y = \sin x$

$y = \cos x$

$y = \tan x$

$y = \cot x$

$y = \sec x$

$y = \csc x$

I hope that this was helpful.

• Well that depends on the six trig functions.

First, Domain is the set of x-values. To find it, think of the left most value traveling to the right most value. Range is the set of the y-values. So, you look bottom to top.

Next, sine and cosine follow similar graphs. If you think about it, you can take sine and cosine of any angle, from negative infinity to negative infinity. Thus, the Domain = $\left[- \infty , \infty\right]$ or $\mathbb{R}$. As you calculate the sine and cosine of each number, you will see that all values are between -1 and 1. Thus, the Range = $\left[- 1 , 1\right]$.

Since tangent is the ratio of sine to cosine, you have to be careful. As mentioned before, cosine can be 0, but you cannot divide by 0. So, there will be times when the tangent function is undefined, thus the domain is affected. Thus, the Domain = $\mathbb{R}$, except when $x = n \pi \left(n \in \mathbb{N}\right)$. Luckily, the Range is easier. Range = $\mathbb{R}$.

Now, to find secant (sec), try graphing $\frac{1}{\cos} x$. You can do this on a graphing calculator, using Zoom Trig.
For cosecant (csc), graph $\frac{1}{\sin} x$.
For cotangent (cot), graph $\frac{1}{\tan} x$.

I hope this helps.

• The period of any function , imagine it to be a function of say time, is the minimum time upon which it repeats itself. Even if the "time" is say in the plane, you would want it to have the smallest length, as 2 times a period , say is a period, but not the minimal one, which is what you usually mean by a period. Trigonometric functions, are just functions depending on sines and cosines,and the above definition works for them, so if they are suitably normalized the period would be taken to be some rational multiple of 2*pi.

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