My Math Forum  

Go Back   My Math Forum > High School Math Forum > Trigonometry

Trigonometry Trigonometry Math Forum

LinkBack Thread Tools Display Modes
December 3rd, 2016, 03:14 PM   #1
Joined: Dec 2016
From: Romania

Posts: 2
Thanks: 0

Question 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?
flaby is offline  
December 3rd, 2016, 03:31 PM   #2
Senior Member
romsek's Avatar
Joined: Sep 2015
From: USA

Posts: 1,932
Thanks: 1000

you can if you know the hypotenuse (in this case the radius of the circle) is 1.
romsek is offline  
December 3rd, 2016, 03:49 PM   #3
Senior Member
SenatorArmstrong's Avatar
Joined: Nov 2015
From: United States of America

Posts: 167
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 x-axis. 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.
SenatorArmstrong is offline  
December 3rd, 2016, 04:53 PM   #4
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.
HisNameForever is offline  

  My Math Forum > High School Math Forum > Trigonometry

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

Copyright © 2018 My Math Forum. All rights reserved.