July 18th, 2018, 04:37 AM  #1 
Senior Member Joined: Nov 2011 Posts: 230 Thanks: 2  trigonometric functions
What is the meaning of sign of trigonometric function in the Cartesian Coordinate System? in this link: https://en.wikipedia.org/wiki/Quadrant_(plane_geometry) Last edited by skipjack; July 18th, 2018 at 12:50 PM. 
July 18th, 2018, 04:47 AM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,889 Thanks: 768 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
$\displaystyle \sin(\theta) > 0 \implies y > 0 \implies \text{Q1 or Q2}$ $\displaystyle \sin(\theta) < 0 \implies y < 0 \implies \text{Q3 or Q4}$ $\displaystyle \cos(\theta) > 0 \implies x > 0 \implies \text{Q1 or Q4}$ $\displaystyle \cos(\theta) < 0 \implies x < 0 \implies \text{Q2 or Q3}$ Combining these gives the tangent quadrants: $\displaystyle \tan(\theta) > 0 \implies \frac{y}{x} > 0 \implies \text{Q1 or Q3}$ $\displaystyle \tan(\theta) < 0 \implies \frac{y}{x} < 0 \implies \text{Q2 or Q4}$ Dan Last edited by skipjack; July 18th, 2018 at 12:50 PM.  
July 18th, 2018, 05:36 AM  #3 
Senior Member Joined: Nov 2011 Posts: 230 Thanks: 2  Name of the representation
Is this called polar representation?
Last edited by skipjack; July 19th, 2018 at 07:31 AM. 
July 18th, 2018, 09:44 AM  #4 
Senior Member Joined: Nov 2011 Posts: 230 Thanks: 2 
I figure out that difference between what you explain is that polar representation is to size that can be different from 1 (or the unit) like: x = var.cos(alpha) = 3cos(alpha) [notice about the 3] and In your equations are the kind that 3 is came instead of 1. The 1 is the unit as in the representation: x = 1cos(alpha) = cos(alpha). Right? Last edited by skipjack; July 19th, 2018 at 07:33 AM. 
July 19th, 2018, 07:45 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 19,712 Thanks: 1806 
The values for x, y and the radius of the circle must effectively use the same unit of length. This means, for example, that if the circle's radius is r, x = r*cos(θ) and y = r*sin(θ). It follows that using a radius of 1 simplifies the expressions without changing the value of cos(θ), sin(θ) or tan(θ).

July 20th, 2018, 06:41 AM  #6 
Member Joined: Oct 2017 From: Japan Posts: 62 Thanks: 3 
Once you understand how the unit circle works, it is quite easy to get the sine and cosine as projections onto the x and yaxis. Last edited by skipjack; July 22nd, 2018 at 07:10 AM. 
July 21st, 2018, 05:45 PM  #7 
Newbie Joined: Jul 2018 From: Los Angeles Posts: 2 Thanks: 1 
Did somebody say Radius of one?

July 21st, 2018, 06:43 PM  #8 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,889 Thanks: 768 Math Focus: Wibbly wobbly timeywimey stuff.  
July 22nd, 2018, 04:58 AM  #9 
Newbie Joined: Jul 2018 From: Los Angeles Posts: 2 Thanks: 1  

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