Derivs of Trig

1. Block 1
Differentiation 2

2. Just when you thought it was
safe to go back to the classroom
Differentiation 2
(The Sequel)

3. What is to be learned?
• How to find derivatives of sin x and cos x

4. +
–
+
f(x) = sinx
f/
(x) = cosx

5. +–
f(x) = cosx
f/
(x) = -sinx

6. f(x) = sinx
f/
(x) = cosx
f(x) = cosx
f/
(x) = sinx–

7. f(x) = 8sinx
f/
(x) = 8cosx
f(x) = 11cosx
f/
(x) = -11sinx

8. f(x) = -3sinx
f/
(x) = -3cosx
f(x) = -5cosx
f/
(x) = 5sinx

9. 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

10. Calculus and Trig
Always use radians

11. f(x) = 5sinx
f/
(x) = 5cosx
f/
(π
/6)?
f/
(π
/6) = 5cos (π
/6)
= 5(√3
/2)
= 5√3
/2

12. f(x) = 3sinx
f/
(x) = 3cosx
f/
(π
/4)?
f/
(π
/6) = 3cos (π
/4)
= 3(1
/√2)
= 3
/√2

13. f(x) = 2cosx
f/
(x) = -2sinx
f/
(π
/6)?
f/
(π
/6) = -2sin (π
/6)
= -2(1
/2)
= -1

14. Gradient of tangent to y = 4cosx
at x = π
y = 4cosx
dy
/dx = -4sinx
at x= π, m= -4sinπ
m = 0
π
m = 0

15. 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

16. 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