3.8 Derivatives of Inverse Trigonometric Functions What you’ll learn about… Derivatives of Inverse Functions Why? The relationship between the graph of a function and its inverse allows us to see the relationship between their derivatives.

Derivatives of Inverse Trigonometric functions

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Where do these come from? Derivative of the arcsine… We can simplify using the identity

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What about the sec -1 x?

Finding the derivative of the Arctangent Using the trig identity

A particle moves along the x-axis so that its position at any time t ≥ 0 is given by x(t) = tan -1 (t 2 ). Find the velocity at the t = 1. Evaluate at t = 1.

What can we do with these derivatives? We can find slopes and write the equations of tangent & normal lines to the curve at x=a! Find an equation for the line tangent to the graph of y = cot -1 x at x = -1 How? Use the given equation and x = a to find a point on the curve. Find f ’ and evaluate it at a to get the slope of the tangent. Recall that -1/ a is the slope of the normal line. Write an equation in point slope form, simplify if needed.

Homework p170 Quick Review 1-10 Exercises 3-27 (3n, nЄI)

Today’s Agenda Correct Homework: Q & A Free Response Practice: No Calculator Homework Page 170 Exercises (3n, nЄI), 35-40