# What are these specific trigonometric functions used for?

$\cos\theta$, $\sin\theta$, $\tan\theta$, $\csc\theta$, $\cot\theta$, $\sec\theta$

What are these all used for? Are they used to find the measure of a give angle provided the measurements of other angles or legs of a right triangle? Please clarify for me.

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## 2 Answers

All of the functions you have asked about are called Trigonometric functions. They are all based on relationships between angles and sides of triangles. As such they are related. For example $\tan(x)=\sin(x)/\cos(x)$. These functions don't provide a measure of an angle, as you can see from the $\tan(x)$ example. However, there inverse functions do.

However, overtime, they were found very useful in many of the sciences we use today such as Astronomy, Electronics, Mechanics, Wave Theory, Telecom, Navigation Systems,etc.

You can find good detail in this link: Wiki-Trig

Edit: A somewhat related question came about lately in here: What is so special about Sin(x)

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Strictly geometrically, these are the lengths of various line segments in a unit circle with a given angle $\theta$ inscribed, see e.g. http://en.wikipedia.org/wiki/File:Circle-trig6.svg

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