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Derivatives of Trig Functions

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

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Derivatives of Trig Functions

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

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

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

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

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

  6. Derivatives of trig functions • The derivatives of all six trig functions:

  7. Trig Identities

  8. Example 1 • Find if

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

  10. Example 2 • Find if

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

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

  13. Example 3 • Find if .

  14. Example 3 • Find if .

  15. Example 3 • Find if .

  16. Example 3 • Find if .

  17. 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 .

  18. 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 .

  19. 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.

  20. 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.

  21. 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.

  22. Class work • Section 2.5 • Page 172 • 2-16 even

  23. Homework • Section 2.5 • Page 172 • 1-27 odd • 31

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