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How to Solve Composite Inverse Trig Functions

Inverse trig functions return a value that is equal to the angle required to produce the value passed to the function. A composite function is a function whose value is dependent on the value returned from another function. This topic is first encountered in Calculus II courses prior to the introduction of integration by trigonometric substitution. Inverse trig functions are used in many fields ranging from navigation to Fourier transforms.

Instructions

- 1
  Determine the inner and outer functions. For example, in the composite function ArcCos (sin (45)), the inner function, commonly referred to as g(x), is sin (45). The outer function in this pair is Cos (g(x)).
- 2
  Evaluate the inner function. The sin (45) = √(2) / 2.
- 3
  Take the returned value from the inner function and pass it to the outer function. Specifically, ArcCos (sin (45)) = ArcCos ( √(2) / 2 ).
- 4
  Evaluate the outer function. In conclusion, ArcCos ( √(2) / 2 ) = 45 degrees.

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