Derivatives of Trig Functions

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Presentation transcript:

Derivatives of Trig Functions Objective: Memorize the derivatives of the six trig functions

Derivative of the sin(x) The derivative of the sinx is: Graph the sin function and try to draw the graph of the derivative. What does this graph look like?

Derivative of the sin(x) The derivative of the sinx is:

Derivative of the sin(x) The derivative of the sinx is: Lets look at the two graphs together.

Derivative of the cos(x) The derivative of the cosx is:

Derivative of the cos(x) The derivative of the cosx is: Lets look at the two graphs together.

Derivatives of trig functions The derivatives of all six trig functions:

Trig Identities

Trig Identities

Trig Identities

Example 1 Find if

Example 1 Find if We need to use the product rule to solve.

Example 2 Find if

Example 2 Find if We need to use the quotient rule to solve.

Example 2 Find if We need to use the quotient rule to solve.

Example 3 Find if .

Example 3 Find if .

Example 3 Find if .

Example 3 Find if .

Example 4 On a sunny day, a 50-ft flagpole casts a shadow that changes with the angle of elevation of the Sun. Let s be the length of the shadow and the angle of elevation of the Sun. Find the rate at which the shadow is changing with respect to when . Express your answer in degrees.

Example 4 On a sunny day, a 50-ft flagpole casts a shadow that changes with the angle of elevation of the Sun. Let s be the length of the shadow and the angle of elevation of the Sun. Find the rate at which the shadow is changing with respect to when . The variables s and are related by or .

Example 4 We are looking for the rate of change of s with respect to . In other words, we are looking to solve for . In this example, is the independent var.

Example 4 We are looking for the rate of change of s with respect to . In other words, we are looking to solve for . In this example, is the independent var.

Example 4 We are looking for the rate of change of s with respect to . In other words, we are looking to solve for . In this example, is the independent var.

Example 4 We are looking for the rate of change of s with respect to . In other words, we are looking to solve for . In this example, is the independent var.

Example 4 We are looking for the rate of change of s with respect to . In other words, we are looking to solve for . In this example, is the independent var. Both answers can’t be right. Which one is?

Example 4 We are looking for the rate of change of s with respect to . In other words, we are looking to solve for . In this example, is the independent var.

Class work Section 2.5 Page 172 2-16 even

Homework Section 2.5 Page 172 1-27 odd 31