Thursday, November 12, 2009

Graphing Sin, Cos and Tan functions

The graphs of the 3 trigonometric ratios are graphed with the values of that particular ratio at x radians

(This is a sine wave, very relevant to what im talking about)

The 3 functions are:

f(x) = sinx

f(x) = cosx

f(x) = tanx

These graphs have some similar properties:

1. All are periodic, meaning they repeat themselves at certain intervals

The graphs of sin and cos repeat on intervals of k2II <--- (yes, that is pie)

The graph of tanx repeats at intervals of kII

*where k is an element of the integers

*transformations may affect the intervals on which they repeat


When graphing these functions, it is easiest to use 5 key angles (values of x)

0, 90, 180, 270, 360

In other words

0, II/2, II, 3II/2, 2II

In the cos and sin graphs these will gives us nice heights of 1 or 0, making it easy for us to graph it.

The "new graph" tanx is weirder.

Knowing the trig identity

tanx = sinx


it can help us to graph tan

With our knowledge of reciprocal functions we can attempt to graph this. Since cosx is in the denominator, any occurrences of a zero value will create a vertical asymptote at that point.

In the case of cos, it has zero values at II/2 and 3II/2 radians (+ or - k amounts of II)

If the numerator of the function = 0, we know an x intercept will occur there, so plot the x intercepts

Tanx = 1 at II/4 radians, these are nice points to plot. Put everything on the graph and connect the dots and make sure to put arrows on the end of the lines, and you should have an approximation of the graph of the function f(x) = tanx

All these graphs are made by unwrapping the unit circle, i feel like it was important to say that. If you got all the way here thanks for reading this, I dun know if it helpd.

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