COMPOUND ANGLE FORMULAS
Recall the unit circle:
r=1
y

(cos,sin)
x

x
compound angle:
an angle that is created by adding or subtracting
two or more angles
Determine a formula for calculating cos(a – b) using the given diagram:
Using Cosine Law:
c2 = a2 + b2 – 2abcosC
Using Distance Formula:
c  (y 2  y 1 ) 2  (x 2  x 1 ) 2
Equate and Simplify:
y
COMPOUND ANGLE FORMULAS:
sin(a  b) = sina cosb  cosa sinb
cos(a  b) = cosa cosb  sina sinb
tan(a  b) =
tan a  tan b
1  tan a tan b
Compound angle formulas can be used, both forward and backward,
to evaluate and simplify trigonometric expressions.
Example 
a)
75o
Example 
a)
Express each angle as a compound angle, using a pair of angles from
the special triangles:
b)
11
12
Determine the exact value of each of the following:
 
cos   
3 4
b)
 5 
tan  
 12 
b)
 19 
sec 

 12 
Example 
Simplify, then evaluate the expression:
cos
7
5
7
5
cos
 sin
sin
12
12
12
12
Example 
Evaluate sin(a + b), where a and b are obtuse angles and
3
5
sina =
and sinb =
.
5
13
Homework: p.400–401 #1 – 6, 8 – 12
(alt. where appropriate)