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Derivatives of Trig functions

Derivatives of Trig functions. Find derivatives of basic trig functions Applications. Derivative of sin x. Recall sin ( a+b )=sin a cos b + sin b cos a and lim h 0 sin h/h =1, lim h 0 (1-cos h )/ h=0 Use in computing derivative of sin:. Conclusion.

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Derivatives of Trig functions

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  1. Derivatives of Trig functions • Find derivatives of basic trig functions • Applications

  2. Derivative of sin x • Recall sin (a+b)=sin a cos b + sin b cos a and limh0 sin h/h =1, limh0 (1-cos h)/h=0 • Use in computing derivative of sin:

  3. Conclusion • Similar arguments work for cosine

  4. Derivative of tangent

  5. Derivatives of all trig functions

  6. Examples

  7. More examples

  8. A word problem • Suppose that the rising sun passes directly over a building that is 90 feet high and let  be the sun’s angle of elevation with respect to the earth. Find the rate at which the length x of the building’s shadow is changing with respect to  when  =/4.

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