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Derivs of trig

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S
Shaun Wilson

The document provides information on how to find the derivatives of trigonometric functions sin(x) and cos(x). It gives the derivatives of common trigonometric functions like f(x) = sin(x), f(x) = cos(x), as well as the derivatives of modified versions with coefficients like f(x) = 8sin(x). It also shows how to find the derivatives of trigonometric functions at specific values by using the trigonometric derivatives and evaluating them at that point. Examples are provided for finding derivatives at values like π/6 and π/4.

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Block 1 Differentiation 2
Just when you thought it was safe to go back to the classroom Differentiation 2 (The Sequel)
What is to be learned? • How to find derivatives of sin x and cos x
+ – + f(x) = sinx f/ (x) = cosx
+– f(x) = cosx f/ (x) = -sinx
f(x) = sinx f/ (x) = cosx f(x) = cosx f/ (x) = sinx–
f(x) = 8sinx f/ (x) = 8cosx f(x) = 11cosx f/ (x) = -11sinx
f(x) = -3sinx f/ (x) = -3cosx f(x) = -5cosx f/ (x) = 5sinx
f(x) = sinx f/ (x) = cosx f(x) = cosx f/ (x) = sinx– Derivatives of Sin and Cos f(x) = -3sinx f/ (x) = -3cosx f(x) = 3cosx + x2 f/ (x) = -3sinx + 2x
Calculus and Trig Always use radians
f(x) = 5sinx f/ (x) = 5cosx f/ (π /6)? f/ (π /6) = 5cos (π /6) = 5(√3 /2) = 5√3 /2
f(x) = 3sinx f/ (x) = 3cosx f/ (π /4)? f/ (π /6) = 3cos (π /4) = 3(1 /√2) = 3 /√2
f(x) = 2cosx f/ (x) = -2sinx f/ (π /6)? f/ (π /6) = -2sin (π /6) = -2(1 /2) = -1
Gradient of tangent to y = 4cosx at x = π y = 4cosx dy /dx = -4sinx at x= π, m= -4sinπ m = 0 π m = 0
rate of change of y = 2sinx + 7x at x = π y = 2sinx + 7x dy /dx = 2cosx + 7 at x= π, rate of change = 2cosπ + 7 = 5 = 2(-1) + 7 Always use radians
Gradient of tangent to y = 3sinx at x = π /3 y = 3sinx dy /dx = 3cosx at x= π /3, m= 3cos (π /3) m = 3( ½ ) π /3 m = 3 /2 m = 3 /2 Key Question

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Derivs of trig