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Math 151 Section 3 4 Derivatives of Trig Functions Special Limits of Trigonometric Functions sin x 1 x 0 x lim cos x 1 0 x 0 x lim Example Find the following limits A lim x 0 B lim x 0 C lim x 0 D lim x 0 sin 2x 3x sin 8x sin 9x cot 2x csc x tan 2 4x x2 Math 151 Trigonometric Derivative Rules d d sin x cos x tan x sec 2 x dx dx d sec x sec x tan x dx d cos x sin x dx d csc x csc x cot x dx d cot x csc 2 x dx Example Find the following derivatives A y 5tan x 3sec x B y sin x 1 cos x C y x 3 cot x Example For what value s of x does y x 2cos x have a horizontal tangent line
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