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
| Inverse Trigonometric Functions When you are given an angle X, trigonometry is used to compute Sin(X), Cos(X), and Tan(X). When the value of Sin(X) is given, for example Sin(X) = 0.2, the inverse sine function provides the value of X. Sin-1(X) is known as the inverse sine function and it is NOT equal to 1/Sin(X). X = Sin-1(0.2) = 11.5° This function is not single valued. In the range of 0° to 360°, the Sine function is positive in the first and second quadrant. So, X = 11.5°, but it also equals 180° - 11.5° which is 168.5°. For more information, you should inspect the inverse graphs page. When the cosine of angle X is known, such as Cos(X) = 0.2, the inverse cosine function finds the value of X. Cos-1(X) is known as the inverse cosine function as is NOT equal to 1/Cos(X). X = Cos-1(0.2) = 78.5° This function is also not single valued, and since cosine is positive in the first and fourth quadrants, the other value would be 360° - 78.5° which is 281.5°. When the tangent of angle X is known, Tan(X) = 0.2, the inverse tangent function can solve for the value of X. Tan-1(X) is the known inverse tangent function and is NOT equal to 1/Tan(X). X = Tan-1(0.2) = 11.3° However, this function is not single valued, and since the tangent function is positive in the first and third quadrants, the other value would be 180° + 11.3° which is 191.3°. |
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