Inverse Trigonometric Functions OBJECTIVES: Evaluate the inverse trigonometric functions Evaluate the compositions of trigonometric functions

Inverse functions RECALL: for a function to have an inverse function, it must be one-to-one – that is, it must pass the Horizontal Line Test. So consider the graphs of the six trigonometric functions, will they pass the Horizontal Line Test?

Inverse Trigonometric functions However, if you restrict the domain of the trig functions, you will have a unique inverse function. But in such a restriction, the range will be unchanged, it will take on the full range of values for the trig function. Therefore, allowing the trig function to be one-to-one. The INVERSE SINE FUNCTION is defined by where the domain is and the range is

EX 1: If possible, find the exact value

Inverse Trigonometric functions The INVERSE COSINE FUNCTION is defined by where the domain is and the range is The INVERSE TANGENT FUNCTION is defined by where the domain is and the range is

EX 2: If possible, find the exact value

Inverse Trigonometric Functions Domain Range Quadrant of the Unit Circle Range Values come from I and IV I and II

EX 3: Use a calculator to approximate the value, if possible

EX4: Find the exact value of the composition function

EX4: Find the exact value of the composition function B)

EX4: Find the exact value of the composition function

EX4: Find the exact value of the composition function