PreCalSection6.1 1
Math 1330
Sections 6.1 and 6.2
Combining Angle Formulas
These formulas are labeled in terms of angles, and they work for both angles in degrees
and angles or numbers in radians.
Sum and Difference Formulas
1.
sin( ) sin( )cos( ) cos( )sin( )
s t s t s t
+ = +
2.
sin( ) sin( )cos( ) cos( )sin( )
s t s t s t
− = −
3.
cos( ) cos( )cos( ) sin( )sin( )
s t s t s t
+ = −
4.
cos( ) cos( ) cos( ) sin( )sin( )
s t s t s t
− = +
5.
tan( ) tan( )
tan( )
1 tan( ) tan( )
s t
s t
s t
+
+ = −
6.
tan( ) tan( )
tan( )
1 tan( ) tan( )
s t
s t
s t
−
− = +
Double Angle Formulas
7.
sin(2 ) 2sin( )cos( )
θ θ θ
=
8.
2 2
cos(2 ) cos ( ) sin ( )
θ θ θ
= −
9.
2
2tan( )
tan(2 )
1 tan ( )
θ
θ
θ
=−
Half Angle Formulas
10.
1 cos( )
sin( )
2 2
s s
−
= ±
11.
1 cos( )
cos( )
2 2
s s
+
= ±
12.
sin( )
tan( )
2 1 cos( )
s s
s
=+
The choice of signs in formulas 10 and 11 depends on the quadrant in which the angles in
question terminate.
Reduction Formulas – these formulas follow straight from the formulas above, but are
useful to list to show how the functions are related.
13.
cos( ) sin( )
2
π
θ θ
− =
14.
sin( ) cos( )
2
π
θ θ
− =
