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Section 3 4 Derivatives of trigonometric functions Theorem lim sin 0 0 Theorem lim cos 1 0 Theorem lim 0 sin 1 Corollary lim cos 1 0 0 Example 1 Find each limit 1 cos 2x a lim x 0 2x2 sin 5x x 0 2x b lim sin 4x x 0 sin 3x c lim 1 tan 3x x 0 sin 2x d lim Derivatives d sin x cos x dx d cos x sin x dx d 1 tan x sec2 x dx cos2 x 1 d cot x 2 csc2 x dx sin x d csc x csc x cot x dx d sec x sec x tan x dx dy dx a y cos x 2 tan x Example 2 Find b y 2x x cot x 2 c y x csc x cos x at which the tangent is horizontal Example 3 Find the points on the curve y 2 sin x 3
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