3.5 Derivatives of Trig Functions
London Bridge, Lake Havasu City, Arizona
Photo by Vickie Kelly, 2001
Greg Kelly, Hanford High School, Richland, Washington
Consider the function
y  sin  
 slope
We could make a graph of the slope:



2
1
0
1
Now we connect the dots!
0

2
The resulting curve is a cosine curve.

1
0
d
sin  x   cos x
dx

We can do the same thing for y  cos  
 slope


The resulting curve is a sine curve that has
been reflected about the x-axis.

2
0

2

0
1
0
1
0
d
cos  x    sin x
dx

We can find the derivative of tangent x by using the
quotient rule.
d
tan x
dx
cos 2 x  sin 2 x
cos 2 x
d sin x
dx cos x
1
cos 2 x
cos x  cos x  sin x    sin x 
sec 2 x
cos 2 x
d
tan  x   sec2 x
dx

DERIVATIVE OF TRIGONOMETRIC
FUNCTIONS
d
sin x  cos x
dx
d
cot x   csc 2 x
dx
d
cos x   sin x
dx
d
sec x  sec x  tan x
dx
d
tan x  sec 2 x
dx
d
csc x   csc x  cot x
dx

EXAMPLES:
EXAMPLES:
EXAMPLES:
Examples