
Trigonometry Trigonometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
December 3rd, 2016, 03:14 PM  #1 
Newbie Joined: Dec 2016 From: Romania Posts: 2 Thanks: 0  Trying to understand sin and cos
I'm trying to understand sin and cos. What exactly are them. I found this graph on the internet : But it seems wrong. In a right triangle you can't find cathetus knowing just sin and cos of an angle. So what exactly is this graph trying to represent? Thanks! 
December 3rd, 2016, 03:31 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,790 Thanks: 922 
you can if you know the hypotenuse (in this case the radius of the circle) is 1.

December 3rd, 2016, 03:49 PM  #3 
Senior Member Joined: Nov 2015 From: United States of America Posts: 165 Thanks: 21 Math Focus: Calculus and Physics 
Sin and Cos are both trigonometric functions. The graph you included is the unit circle. It is a circle with a radius of 1 that is placed at the origin of a Cartesian plane. The beauty of this is I can pick any point on that circle, and the x coordinate of that point with be my cos and the y coordinate will be my sin. I then draw a line from that point to the center of the circle (this will be my hypotenuse which will always equal 1). From my point, I also draw a vertical line to the xaxis. This vertical line is sin. From the base of that vertical line I can then draw a line back to the origin. This horizontal line is my cos. We have now formed a triangle (like the one in your picture you showed us). Armed with the Pythagorean theorem, law of sines, law of cosines, etc, we can do a ton of cool things from here to solve triangles. There are geniuses on here that will certainly laugh at my explanation, so take it with a grain of salt. Trigonometry is one of my favorite branches of mathematics so I figured I would leave my two cents. 
December 3rd, 2016, 04:53 PM  #4 
Newbie Joined: Dec 2016 From: Oregon Posts: 8 Thanks: 0  sin(theta) & cos(theta)
The sine of a degree, for example in your graph, sin(45, is the same as the saying to sine of 45 degrees is the opposite over hypotenuse. So sine of 45 degrees equals square root 2 over 2. sqrt(2)/2. Sine is also the y value of the point of your radius. On your graph it is also the length of the red line that has sine(theta) next to it.


Tags 
cos, sin, understand 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Please help me to understand  nautudent  Algebra  7  May 2nd, 2015 04:44 AM 
Help me understand this  bradhills  Algebra  1  February 21st, 2013 12:48 PM 
need help to understand  ment0smintz  Calculus  6  February 18th, 2013 12:07 PM 
Help me understand this?  goodjobbro  Number Theory  13  December 25th, 2012 06:36 PM 
I don't understand this...  johnny  Algebra  1  July 21st, 2009 01:18 AM 