Inverse Trigonometric Functions OBJECTIVES Evaluate the inverse trigonometric

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 �A) �B) �C) �D)

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 �A) �B) �C) �D)

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

EX 3: Use a calculator to approximate the value, if possible �A) �B) �C)

EX 4: Find the exact value of the composition function �A)

EX 4: Find the exact value of the composition function �B)

EX 4: Find the exact value of the composition function �C)

EX 4: Find the exact value of the composition function �D)