Cos & Sin: Learn How to Work With Them

[-Physician]

Yes, I have searched on google/youtube but I want to know how to work with them in tasks for example ramp friction
$f=mgcos0$

 

[genericusrnme]

Cos and Sin are your basic trigonometric functions

If you have a line going from (0,0) to a point (x,y), which is a distance $r=\sqrt{x^2+y^2}$ from the center, then the angle between the horizontal line and the line from (0,0) to (x,y) is related to the components a and b by;
$Cos[\theta]=\frac{x}{r}$
$Sin[\theta]=\frac{y}{r}$
There is also a function, Tan which is related to Cos and Sin by
$Tan[\theta]=\frac{Sin[\theta]}{Cos[\theta]}$
If we use the definitions earlier of the relations between Cos and Sin, and and compoents a,b we get
$Tan[\theta]=\frac{y}{x}$

If you measure the angle $\theta$ from the horizontal then $r\ Cos[\theta]$ gives you the x component of a vector of length r and at an angle $\theta$ to the horizontal. $r\ Sin[\theta]$ gives you the y component.

The trig functions are most easily understood as being projections onto the coordinate axes (imo)

What is it, in particular, that you're having trouble with in understanding the trig functions?

 

[-Physician]

Got it now, thank you very much!

 

[-Physician]

Just 1 more question, what to do if we have $cos30$ for e.x

 

[SHISHKABOB]

you should look up the unit circle

basically there are some angles that have well-defined values in regards to the trigonometric functions. cos(30°) for example is equal to 1/2

while other values, like, say cos(42°) is equal to some weird fraction which is about 0.743

the well defined angles are basically all of the multiples of 30° and 45°

if the angle you have is one of these angles, then (if you have the unit circle memorized) you just pop out the fraction. But if it's some other angle, then you stick it into your calculator.

 

[QuarkCharmer]

Check out the first couple of videos here (they are only like 10 min long each).
http://www.khanacademy.org/#trigonometry

Then you should have a pretty good idea what they represent.

 

[genericusrnme]

Just 1 more question, what to do if we have $cos30$ for e.x

Cos(30) will give you the x component of a unit vcetor pointing 30 degrees up from the horizontal.

Cos(30) is just a number on it's own

 

[shyguy79]

sin is something you shouldn't do cos it's bad!

The guys have definitely covered it though!