Variations of

Variations of cos( A) ⋅ cos( B) + sin( A)
⋅sin( B)
(Side #1)
On your calculator, graph f(x) using the following window. Use the graphs to write a
simpler equation for f(x). (Numbers 1 and 2 have been graphed for you.) Remember, if
y = sin( b⋅x)
, the b stands for the number of cycles seen from 0 to 2π.
1) f ( x) = cos( x) ⋅ cos( x) + sin( x)
⋅sin( x ) 2) f ( x) = cos( x) ⋅cos( x) −sin( x) ⋅ sin( x)
f( x ) = __________________
f( x ) = __________________
3) f ( x) = cos(2 x) ⋅ cos( x) + sin(2 x)
⋅sin( x ) 4) f ( x) = cos(2 x) ⋅cos( x) −sin(2 x) ⋅ sin( x)
f( x ) = __________________
f( x ) = __________________
5) f ( x) = cos(3 x) ⋅ cos(2 x) + sin(3 x) ⋅ sin(2 x)
6) f ( x) = cos(3 x) ⋅cos(2 x) −sin(3 x) ⋅ sin(2 x)
f( x ) = __________________
f( x ) = __________________
7) f ( x) = cos(6 x) ⋅ cos(2 x) + sin(6 x)
⋅sin(2 x) 8)
f ( x) = cos(6 x) ⋅cos(2 x) −sin(6 x)
⋅sin(2 x )
f( x ) = __________________
f( x ) = __________________
For numbers 9 and 10, use numbers 1 – 8 to make your conjecture.
9) f ( x) = cos( A) ⋅ cos( B) + sin( A)
⋅sin( B ) 10) f ( x) = cos( A) ⋅cos( B) −sin( A) ⋅ sin( B)
f( x ) = __________________
f( x ) =
__________________

Variations of sin( A) ⋅ cos( B) + cos( A)
⋅sin( B)
(Side #2)
On your calculator, graph f(x) using the following window. Use the graphs to write a
simpler equation for f(x). (Numbers 1 and 2 have been graphed for you.) Remember, if
y = sin( b⋅x)
, the b stands for the number of cycles seen from 0 to 2π.
1) f ( x) = sin( x) ⋅ cos( x) + cos( x)
⋅sin( x ) 2) f ( x) = sin( x) ⋅cos( x) −cos( x) ⋅ sin( x)
f( x ) = __________________
f( x ) = __________________
3) f ( x) = sin(2 x) ⋅ cos( x) + cos(2 x)
⋅sin( x ) 4) f ( x) = sin(2 x) ⋅cos( x) −cos(2 x) ⋅ sin( x)
f( x ) = __________________
f( x ) = __________________
5) f ( x) = sin(3 x) ⋅ cos(2 x) + cos(3 x)
⋅sin(2 x ) 6) f ( x) = sin(3 x) ⋅cos(2 x) −cos(3 x) ⋅ sin(2 x)
f( x ) = __________________
f( x ) = __________________
7) f ( x) = sin(3 x) ⋅cos( − x) + cos(3 x)
⋅sin( −x) 8)
f ( x) = sin(3 x) ⋅cos( −x) −cos(3 x)
⋅sin( − x)
f( x ) = __________________
f( x ) = __________________
For numbers 9 and 10, use numbers 1 – 8 to make your conjecture.
9) f ( x) = sin( A) ⋅ cos( B) + cos( A)
⋅sin( B ) 10) f ( x) = sin( A) ⋅cos( B) −cos( A) ⋅ sin( B)
f( x ) = __________________
f( x ) =
__________________