5.6 Inverse Trig Functions and Differentiation Lewis and Clark Caverns, Montana Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 1993

Objectives Develop properties of the six inverse trigonometric functions. Differentiate an inverse trigonometric function. Review the basic differentiation formulas for elementary functions.

Recall inverse functions:

Function Domain Range Quadrants [-1,1] [-π/2, π/2] I & IV [0, π] Trig functions have inverses only in restricted domains. A S C T Function Domain Range Quadrants [-1,1] [-π/2, π/2] I & IV [0, π] I & II (-∞,∞) (0, π) |x|≥1 [0, π], y≠π/2 [-π/2, π/2], y≠0

Inverse trig functions on the calculator:

Look at the six inverse trig functions on p. 374. How would you graph arccscx?

Evaluate each of the following. When you apply properties to inverse trig functions, you have to make sure the x-values are in the domain. Make sure your calculator is in radian mode.

1 x y° b

1 b y° 2

We can use implicit differentiation to find:

We can use implicit differentiation to find: 1 x y° b

Find the derivative.

Find the derivative.

Find the derivative.

Homework 5.6 (page 379) #5-19 odd, 27 – 33 odd, 37, 39, 43-53 odd, 57, 61 p