Trigonometric Functions

Tangent Graph: If x increases by pi/4 (or tau/8), y increases by one. Sine Graph: represents going around a circle and the correlation between altitude and how far "you have gone" around the circumference. Cosine Graph: represents a similar circle-related function.

Sine & Cosine Graphs: For a particular y value, the x values differ by pi/2 (or tau/4) and at every multiple of pi as the x value, the difference between the y values is 1. To get back to the same y value on either graph, go at an interval of 2 pi (or tau) in the x value.

Sine & Cosine Graphs: The graphs intersect at points where: the x value is the product of an odd number "g" and pi/4 and the y value is ±0.707, having the same sign as the x value. Coordinates: (±g*pi/4, ±0.707) Csc and secant have the same x values, but the y values are doubled.

The graphs never all intersect because when sine and cosine's y values are at positive or negative 0.707, tan is ALWAYS at 1.

Tangent and sine intersect at whole multiples of pi (or at tau/2 intervals), but I just cannot find anything interesting about how tangent and [cosine, arctan] intersect. Can you?

sin(x)=cos(x-pi/2) cos(x)=sin(x+pi/2) Turn off particular graphs while reading the notes --- I definitely did when I wrote the notes. There are just too many. Also, you can rearrange notes to make it easier.

Arcsin and arccos reverse the x and y coordinates, which is why their lines are so small (The y coordinates only range from 0-1 and repeat in the same sequence). It is the same case with arctan, but that is a quite different graph.

-y+pi/2=arccos(x) -y+pi/2=arcsin(x) Make one of these equations (Do not do both or the graphs will just translate.) and the graphs will overlap.

Csc is the reciprocal of sine. Secant is the reciprocal of cosine. Cot is the reciprocal of tangent.

Cot and tangent intersect at the same intervals as sine and cosine except at y=±1, not y=±0.707