Trigonometry
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Trigonometry Reference Home Back to Thinkquest Contents
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Definitions of Trigonometric Functions Trigonometric Functions of Sums and Differences Inverse Trigonometric Functions
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Graphs of Trigonometric Functions
Angles are often measured in a common unit of degrees. One full circle equals 360 degrees. But, angles can also be measured in a scientific unit called radians. One full circle equals 2π radians, which equals 360 degrees. Since 360 degrees = 2π radians, π in radians equals 180 degrees and π/ 2 equals 90 degrees. It is understood when given equations such as y = Sin(X) that X is in radians. If not, then they would give a degrees sign. Plotting the Graph of Y = Sin(X) In this equation, Y ranges from -1 to +1 since the Sine of any angle cannot be greater than 1 and cannot be less than -1. Each time the angle X is increased by 2π, the trigonometric functions of X repeat. So, the graph of Y = Sin(X) is a repeating function with a period of 2π. The amplitude of equations when graphed is distance from the X-axis to the highest point on the curve. The amplitude is the number in front of the function either Sin(x) or Cos(x). In this case, the amplitude is 1. The frequency of a graph is the number of times the graph repeats itself in the interval 0 to 2π. The frequency can be found from the equation. It is the number in front of the angle X. In this case, the frequency is also 1. If the equation given is Y = 2Sin(1/2X), then the amplitude is 2, and the frequency is 1/2. To find the period just by looking at the equation, you find the frequency and plug it into the formula: Period = 2π/frequency. The Graph of Y = Sin(X) with an interval of 0≤X≤2π
Plotting Y = Cos(X) The amplitude is 1, the frequency is 1, and the period is 2π.
The Graph of Y = Cos(X) with an interval of 0≤X≤2π
Plotting the Graph of Y = Tan(X) with the interval of 0≤X≤2π Since Tan(X) = Sin(X)/Cos(X), when Cos(X) is zero, the tangent is undefined. This happens when X equals π/2 and 3π/2. "Near" these values, the function is extremely large and approaches infinity. The lines X = π/2 and X = 3π/2 are called asymptotes.
The graph Cot(X) is similar to the graph of Tan(X). The only differences are that the asymptotes are at X=0 and X= π and the graph is horizontally flipped.
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