HSC Higher Mathematics 2nd Paper Note 7th Chapter Inverse Trigonometric Functions and Trigonometric Equations

HSC Higher Mathematics 2nd Paper Note 7th Chapter Inverse Trigonometric Functions and Trigonometric Equations. In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions are the inverse functions of the trigonometric functions (with suitably restricted domains). Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of the angle’s trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry.

HSC Higher Mathematics 2nd Paper Note 7th Chapter Inverse Trigonometric Functions and Trigonometric Equations

There are several notations used for the inverse trigonometric functions. The most common convention is to name inverse trigonometric functions using an arc- prefix, e.g., arcsin(x), arccos(x), arctan(x), etc. This convention is used throughout the article. When measuring in radians, an angle of θ radians will correspond to an arc whose length is rθ, where r is the radius of the circle. Thus, in the unit circle, “the arc whose cosine is x” is the same as “the angle whose cosine is x”, because the length of the arc of the circle in radii is the same as the measurement of the angle in radians. Similarly, in computer programming languages the inverse trigonometric functions are usually called asin, acos, atan.

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