1. LECTURE 9 of 12 TOPIC : 2.0 TRIGONOMETRY
SUBTOPIC : 2.7 Differentiation
of Trigonometric Functions

2. Learning Outcomes :
Differentiate the implicit and parametric equations which involves trigonometric functions

3. DIFFERENTIATIONS OF IMPLICIT AND PARAMETRIC EQUATIONS WHICH
INVOLVES TRIGONOMETRIC FUNCTIONS
A.DIFFERENTIATION OF IMPLICIT EQUATIONS
EXAMPLE 1 :
Differentiate with respect to x
(a) sin x cos y = 2
(b) y sin x + x = cos y

4. a) sin x cos y = 2
sin x cos y = 0
sin x ( - sin y ) cos y (cos x) = 0
(sin x sin y) = cos x cos y

5. b) y sin x + x = cos y
y cos x + (sin x) = (- sin y)

6. EXAMPLE 2 :
Find for the following
y = x sin x
ln y = (sin x) ln x
SOLUTION :

8. EXAMPLE 3 :
Prove that
if given exy = sin x.

9. SOLUTION :
exy = sin x.

10. B. DIFFERENTIATION OF PARAMETRIC
EQUATIONS
If y = f(t), and x = g(t) are 2 parametric
equations then,

11. EXAMPLE 6 :
Find if

12. x = 2( θ + sin θ ) , y = 2(1- cos θ )

13. EXAMPLE 7 :
Given that x = sin3 2t and y = cos3 2t.
Show that

14. SOLUTION :

15. CONCLUSION A.DIFFERENTIATION OF IMPLICIT EQUATIONS
B. DIFFERENTIATION OF PARAMETRIC
EQUATIONS
If y = f(t), and x = g(t) are 2 parametric
equations then,