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July 18th, 2018, 05:37 AM   #1
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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 01:50 PM.
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July 18th, 2018, 05:47 AM   #2
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Originally Posted by shaharhada View Post
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 01:50 PM.
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July 18th, 2018, 06:36 AM   #3
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Name of the representation

Is this called polar representation?

Last edited by skipjack; July 19th, 2018 at 08:31 AM.
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July 18th, 2018, 10:44 AM   #4
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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 08:33 AM.
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July 19th, 2018, 08:45 AM   #5
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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).
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July 20th, 2018, 07:41 AM   #6
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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 08:10 AM.
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July 21st, 2018, 06:45 PM   #7
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Did somebody say Radius of one?
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July 21st, 2018, 07:43 PM   #8
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Originally Posted by radiusofone View Post
Did somebody say Radius of one?
Personally I like Seven of Nine better.

-Dan
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July 22nd, 2018, 05:58 AM   #9
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Personally I like Seven of Nine better.

-Dan
Then we have come full circle, as that makes two of us.....
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