Like sine is used to get the y coordinate, cosine is used to give the x coordinate, what does tangent and cotangent give?
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Yep I am a programmer
In: 14
In a right triangle Cos and Sin of one of the angles give you the ratio of one of the legs over the hypotenuse, tangent and cotangent of the angle give you the ratio of the two legs over each other. (which is equal to the ratio between cos and sin, since the hypotenuse is the same in those and cancels out).
Tangent and cotangent help us determine the steepness of a line on a graph
It’s like a special way of measuring how much a line is tilting
Hope that helps!
If you plot a point in the unit circle at the given angle and then draw a line tangent to the unit circle through that point the tan of the angle is the length of the segment from the point to where the line intersects the x axis and the cotan is the length from the point to the intersection of the y axis.
here, this is a very useful diagram for all of the trig functions https://i.stack.imgur.com/YNvin.png
so tan is the length of a line tangent to the circle at an angle to where it intersects the x axis, cot is to the y axis, and cosec/sec are how far out that intersect is
If you remember slope intercept form from algebra (y=mx+b) m is the slope of a line calculated as rise/run or (y[1]-y[2])/(x[1]-x[2]). Tangent is the slope of a radius extending from the origin. That radius is the hypotenuse of a right triangle with height sine(theta) and base cosine(theta). Tan is then sin/cos. Cotan is just cos/sin or 1/Tan. Both are useful for working out how lines are oriented relative to a coordinate grid
Tangent is most useful as the arctangent. atan(y/x)=θ, so you can undo the operations of sine and cosine.
Cotangent, as far as I’m aware, only comes into play with integration, which, as a programmer, you would probably just solve computationally.
One way to visualize tangent is if you draw a line centered at the origin with an angle A between the positive x axis and the line, the tangent of A is the slope of that line.
In Cartesian coordinates, tan gives the slope of a vector (and cot gives the inverse slope)
So people tell me that I need to learn algebra to become a programmer, just to clarify, I have been a programmer for 2 years now and 1 year in game development. Just so you know I am a programmer.
Maybe I suck at algebra and probably ok at trigonometry but it a bit annoys me that people look at me like a complete beginner. Not a problem though
As a graphics programmer I don’t think I’ve ever had to deal with cotangent in my career. However, arctangent (and atan2) can be important!
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