Derivatives of Trig Functions

Question 1

Derivative of sinx

Answer 1

cosx

Question 2

Derivative of cosx

Answer 2

-sinx

Question 3

lim(x->0) sinx/x

Answer 3

sinx/x = 1

Question 4

lim(x->0) (cosx-1)/x

Answer 4

(cosx-1)/x = 0

Question 5

Proof of derivative of sinx

Answer 5

lim sin(x+h)-sinx / h
addition/subtraction formula
factor out (sinx(cosh-1))/h
take lim of each part with h in it

Question 6

Proof of derivative of cosx

Answer 6

lim cos(x+h)-cosx / h
addition/subtraction formula
factor out (cosx(cosh-1))/h
take lim of each part with h in it