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July 7th, 2019, 03:16 PM   #1
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COT, CSC, and SEC

Hello,

So, Normally I do Geometry, but something happened that got me curious about trigonometry.

Here is what happened, my brother lent me a book called "Trigonometry, Plane and Spherical." I came across something in the book that I have a question about.

I know about SIN, COS, and TAN functions, but in this book, there are three other functions mentioned called COT, CSC, and SEC. To help explain this, here is an example the book gave:

Imagine a triangle, the angles are A=90, B=42, and C=48. Side BC, (The Hypotenuse,) is 10. So, side AB=7.431448255. Side AC is 6.691306064.

Now, let's take Angle B. According to the book, SIN(42)=0.669130606, COS(42)=0.743144825, and TAN(42)=0.900404044.

It also says that COT(42)=Side AB/Side AC. In other words, 1.110612515

CSC(42)=Side BC/SideAC. In other words, 1.49447655

Sec(42)=SideBC/SideAB. In other words, 1.34563273

Here is my question. What are the COT, CSC, and SEC functions, and how do you use them in mathematics? Can someone help me learn this?

I am continuing to read the book, just so you know. I may learn something from it also.

Jared

Last edited by skipjack; July 7th, 2019 at 06:02 PM.
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July 7th, 2019, 04:24 PM   #2
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Quote:
Originally Posted by jnicholes View Post
Hello,

So, Normally I do Geometry, but something happened that got me curious about trigonometry.

Here is what happened, my brother lent me a book called "Trigonometry, Plane and Spherical." I came across something in the book that I have a question about.

I know about SIN, COS, and TAN functions, but in this book, there are three other functions mentioned called COT, CSC, and SEC. To help explain this, here is an example the book gave:

Imagine a triangle, the angles are A=90, B=42, and C=48. Side BC, (The Hypotenuse,) is 10. So, side AB=7.431448255. Side AC is 6.691306064.

Now, let's take Angle B, According to the book, SIN(42)=0.669130606, COS(42)=0.743144825, and TAN(42)=0.900404044.

It also says that COT(42)=Side AB/Side AC. In other words, 1.110612515

CSC(42)=Side BC/SideAC. In other words, 1.49447655

Sec(42)=SideBC/SideAB. In other words, 1.34563273

Here is my question. What are the COT, CSC, and SEC functions, and how do you use them in mathematics? Can someone help me learn this?

I am continuing to read the book, just so you know. I may learn something from it also.

Jared
$\displaystyle \csc(x) = \frac{1}{\sin(x)}$

$\displaystyle \sec(x) = \frac{1}{\cos(x)}$

$\displaystyle \cot(x) = \frac{1}{\tan(x)} = \frac{\cos(x)}{\sin(x)}$

Frankly, I prefer to just use sin(x) and cos(x) wherever possible.

-Dan

Last edited by skipjack; July 7th, 2019 at 06:07 PM.
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July 8th, 2019, 06:54 AM   #3
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@topsquark, I prefer that too, I'm just trying to expand my knowledge. Thanks for helping me out! I compared what you said to what I said, and they are the same answer. Thanks for helping me out!

Jared
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