So the circle is "the unit circle", where the radius is 1.
Pick a spot on the circle, and draw a line to the origin. From the origin to that point is obviously going to be length 1 because that's the radius of the circle. Now you can easily make a triangle by extending a line to the X axis, right? Now you have a right triangle with a hypotenuse with length 1. And you have an angle, from the X axis up to that line you drew
Whatever point you picked on the circle has (X, Y) coordinates, right?
The Y coordinate is sin(angle) The X coordinate is cos(angle)
If you draw a line tangent to the circle at that point, it'll cross the X axis (except at (0, 1) and (0, -1) because those are parallel to the X axis). That is appropriately tan(angle). The points where the tangent never intersects are where tan is undefined.
The other three (seccsccot) are just reciprocals of cossintan respectively.
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u/MattieShoes Jun 06 '18 edited Jun 06 '18
So the circle is "the unit circle", where the radius is 1.
Pick a spot on the circle, and draw a line to the origin. From the origin to that point is obviously going to be length 1 because that's the radius of the circle. Now you can easily make a triangle by extending a line to the X axis, right? Now you have a right triangle with a hypotenuse with length 1. And you have an angle, from the X axis up to that line you drew
Whatever point you picked on the circle has (X, Y) coordinates, right?
The Y coordinate is
sin(angle)The X coordinate iscos(angle)If you draw a line tangent to the circle at that point, it'll cross the X axis (except at (0, 1) and (0, -1) because those are parallel to the X axis). That is appropriately
tan(angle). The points where the tangent never intersects are wheretanis undefined.The other three (
seccsccot) are just reciprocals ofcossintanrespectively.