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Unformatted text preview: position and released at time t = 0. Its position at any time t ≥ 0 is given by s ( t ) = 5 cos t . What are its velocity and acceleration at time t ? 3 Derivatives of other Basic Trig Functions Because sin x, cos x are diﬀerentiable functions of x , the related functions tan x = sin x cos x , cot x = cos x sin x , sec x = 1 cos x , csc x = 1 sin x are diﬀerentiable at every value of x for which they are deﬁned. We have d dx (tan x ) = d dx (cot x ) = d dx (sec x ) = d dx (csc x ) = Example 5 Show d dx (tan x ) = sec 2 x . Example 6 Find y 00 if y = sec x . Example 7 lim x → √ 2+sec x cos( πtan x ) 4...
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 Spring '08
 FBHinkelmann
 Calculus, Trigonometry, Derivative, Mathematical analysis, Inverse function, Euler's formula, Proofs of trigonometric identities

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