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 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
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 Originally Posted by shaharhada 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)
Remember that $\displaystyle x = \cos(\theta),~y = \sin(\theta)$ maps the unit circle.

$\displaystyle \sin(\theta) > 0 \implies y > 0 \implies \text{Q1 or Q2}$
$\displaystyle \sin(\theta) < 0 \implies y < 0 \implies \text{Q3 or Q4}$

$\displaystyle \cos(\theta) > 0 \implies x > 0 \implies \text{Q1 or Q4}$
$\displaystyle \cos(\theta) < 0 \implies x < 0 \implies \text{Q2 or Q3}$

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
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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 y-axis. 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
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Personally I like Seven of Nine better.

-Dan

July 22nd, 2018, 04:58 AM   #9
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Quote:
 Originally Posted by topsquark Personally I like Seven of Nine better. -Dan
Then we have come full circle, as that makes two of us.....

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