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Trigonometry

The Graph

    The most important use of trigonometry is graphing. The most commonly seen trigonometric graph is the graph of the sound wave. Trigonometric graph is very straightforward if you follow the pattern. Before we dive into the trigonometric graph, there are some basic concepts we need to know. The first one is called "Period". A period is one complete graph of a trigonometric equation without repeating itself. The second one is called "Amplitude". Amplitude is the distance between the ranges of the graph. The third one is called "Domain". Domain is the same as the domain on any graph. The fourth one is called "Range". Range is also the same as the range on any graph. The last one is called the "Frequency". Frequency is equal to 1/Period. After knowing these terms, we can start to graph with trigonometry. We take a trigonometric equation, for example, y = 3 sin 2x. First we can determine this graph is a sine graph. The value 3 in this equation is the amplitude. The value 2 in this equation is divide into the standard period for sine, cosine, secant, and cosecant graphs, which is 2P , to get the period for these graphs. The standard periods for tangent and cotangent graphs are P . If there is a negative sign in front of the equation, you just flip the graph of the positive equation. Below are the standard graphs of most common trigonometric equations.

y = sin x