The Inverse Trigonometric Functions Section 7-6 The Inverse Trigonometric Functions

The Inverse of Tangent From the graph of f(x) = tan x shown on p. 287, we can see that the tangent function is not one-to-one and has no inverse. But, if we restrict x to the interval , the restricted function, which we denote F(x) = Tan x, is one-to-one. Its inverse is denoted and is read “the inverse tangent of x.” Notice that means that tan y = x and .

Inverse Tangent Why does tangent have an inverse in Quadrants 1 and 4 only? Why are not included?

The Inverse of Sine By considering only the solid portion of the graph of g(x) = sin x, as shown on p. 287, we obtain a new function G(x) = Sin x with domain . This graph has an inverse , whose graph is shown on p. 287. Note that means that sin y = x and .

Inverse Sine Why does sine have an inverse in quadrants 1 and 4 only?

The Inverse of Cosine By considering only the solid portion of the graph of h(x) = cos x, as shown on p. 288, we obtain a new function H(x) = Cos x with domain 0 < x < π. This graph has an inverse , whose graph is shown on p. 288. Note that means that cos y = x and 0 < y < π.

Inverse Cosine Why does cosine have an inverse in Quadrants 1 and 2?

Example Use a calculator or table to find the value of each expression to the nearest tenth of a degree and to the nearest hundredth of a radian. b. c.

Example Without using a calculator or table, find the value of each expression in radians. b. b. c.

Example Evaluate each expression without using a calculator

Example Find an approximate value and the exact value of csc ( (-0.4))