We will use the following identities to calculate the derivatives of sin x and cos x
Chapter 3, Problem 66(choose chapter or problem)
We will use the following identities to calculate the derivatives of sin x and cos x: sin(a + b) = sin a cos b + cos a sin b cos(a + b) = cos a cos b sin a sin b. 3.5 THE TRIGONOMETRIC FUNCTIONS 155 (a) Use the definition of the derivative to show that if f(x) = sin x, f (x) = sin x lim h0 cos h 1 h + cos x lim h0 sin h h . (b) Estimate the limits in part (a) with your calculator to explain why f (x) = cos x. (c) If g(x) = cos x, use the definition of the derivative to show that g (x) = sin x.
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