When trying to remember the reciprocals of ""sin"", ""cos"", ""tan"", what is the best way to remember which divides into which?
csc(theta) = 1 / sin(theta)
sec(theta) = 1 / cos(theta)
cot(theta) = 1 / tan(theta).
There is only one 'co' to a pair.
On a unit circle, when the angle is more than 180 degrees, how can you determine the ""sin"", ""cos"", and ""tan""?
Figure out what quadrant the angle is in, and figure out when the angle occurs on the unit circle whether x and y are respectively positive or negative.
That will tell you whether each function (sin(theta) = y, cos(theta) = x, tan(theta) = y / x) is positive or negative.
Then find the sine, cosine and tangent of the reference angle (the angle to the closer part of the x axis), and apply the correct sign (+ or - ) to each.
Is there a way to automatically know what the sin, cos, and tan is for any given angle?
For the special angles 0, pi/6, pi/4, pi/3, pi/2, etc., the special-angle triangles determine the x and y values on the unit circle, and allow you to express the exact values of the functions for these angles.
For certain other angles we will see in the next chapter how to use double-angle, half-angle, sum-of angle formulas, and others, to find exact values.
However for almost all angles, the only other practical way is to use approximate formulas that arise from calculus. Fortunately your calculator has those methods built in, and you can just use it for those angles.
When making a graph of sin, cos, and tan, are they all similar in construction as in they all form a sort of wave?
To construct the basic graphs, you need to use the unit-circle picture and the special angles. Make a table for whichever function you are trying to graph. Note also that as theta approaches 'vertical' (i.e., pi/2 or 3 pi / 2, or 90 deg and 270 deg) the magnitude of the tangent approaches infinity.
Then using the table, you can construct the graph.
You will find that the sin and cos give you wavelike graphs with basic period 2 pi.
The tangent function has period pi, half the period of the sine and cosine functions, and has vertical asymptotes every pi units.