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In this chapter we will expand this list by adding six new rules for the derivatives of the six trigonometric functions: Dxhsin(x)i Dxhtan(x)i Dxhsec(x)i Dxhcos(x)i Dxhcsc(x)i Dxhcot(x)i. This will require a few ingredients. First, we will need the addition formulas for sine and cosine (Equations 3.12 and 3.13 on page 46):
Calculus: Brief Intro to Trig Derivatives Includes notes, examples, formulas, and practice worksheet (with solutions)
Derivatives of Trigonometric Functions 1. d dx sinx= cosx 2. d dx cosx= sinx 3. d dx tanx= sec2 x 4. d dx secx= secxtanx 5. d dx cotx= csc2 x 6. d dx cscx= cscxcotx Useful Trigonometric Identities 1. sin 2 +cos = 1 2. 1+tan 2 = sec
Derivatives of Trigonometric Functions. Before discussing derivatives of trigonmetric functions, we should establish a few important iden-tities. First of all, recall that the trigonometric functions are defined in terms of the unit circle.
TRIGONOMETRIC DERIVATIVES AND INTEGRALS. R. STRATEGY FOR EVALUATING sinm(x) cosn(x)dx. If the power n of cosine is odd (n = 2k + 1), save one cosine factor and use cos2(x) = 1 express the rest of the factors in terms of sine: Z. sinm(x) cosn(x)dx = sinm(x) cos2k+1(x)dx = = Then solve by u-substitution and let u = sin(x). sin2(x) to.
In this section we will look at the derivatives of the trigonometric functions sinx; cosx; tanx ;secx; cscx; cotx: Here the units used are radians and sinx= sin(xradians).
Formulas and theorems 1. A function y=f(x) is continuous at x=a if i. f(a) exists ii. exists, and iii. 2. Even and odd functions 1. A function y = f(x) is even if f(-x) = f(x) for every x in the function's domain. Every even function is symmetric about the y-axis. 2.
