1. 7.3 Double Angle, Half Angle, and
Product Sum Formulas
Day 2
Product to Sum & Sum to Product Formulas
(on your help sheet)
Mark 12:30
Love the Lord your God with all your heart and with all
your soul and with all your mind and with all your
strength.'

2. Express sin ( 2x ) sin ( 4x ) as a trig sum

3. Express sin ( 2x ) sin ( 4x ) as a trig sum
1
sin ( 2x ) sin ( 4x ) = ⎡ cos ( 4x − 2x ) − cos ( 4x + 2x ) ⎤
⎣ ⎦
2

4. Express sin ( 2x ) sin ( 4x ) as a trig sum
1
sin ( 2x ) sin ( 4x ) = ⎡ cos ( 4x − 2x ) − cos ( 4x + 2x ) ⎤
⎣ ⎦
2
1 1
= cos ( 2x ) − cos ( 6x )
2 2

5. Use a product to sum formula to find sin15°cos15°

6. Use a product to sum formula to find sin15°cos15°
1
sin15°cos15° = [ sin 30° + sin 0° ]
2

7. Use a product to sum formula to find sin15°cos15°
1
sin15°cos15° = [ sin 30° + sin 0° ]
2
1 ⎛ 1 ⎞
= ⎜ + 0 ⎟
2 ⎝ 2 ⎠

8. Use a product to sum formula to find sin15°cos15°
1
sin15°cos15° = [ sin 30° + sin 0° ]
2
1 ⎛ 1 ⎞
= ⎜ + 0 ⎟
2 ⎝ 2 ⎠
1
=
4

9. Write sin (11x ) + sin ( 5x ) as a product

10. Write sin (11x ) + sin ( 5x ) as a product
11x + 5x 11x − 5x
sin (11x ) + sin ( 5x ) = 2sin cos
2 2

11. Write sin (11x ) + sin ( 5x ) as a product
11x + 5x 11x − 5x
sin (11x ) + sin ( 5x ) = 2sin cos
2 2
= 2sin ( 8x ) cos ( 3x )

12. Verify the identity:
sin ( 4x ) + sin ( 2x ) sin ( 3x )
=
sin ( 2x ) sin ( x )

13. Verify the identity:
sin ( 4x ) + sin ( 2x ) sin ( 3x )
=
sin ( 2x ) sin ( x )
2sin ( 3x ) cos ( x )
=
2sin ( x ) cos ( x )

14. Verify the identity:
sin ( 4x ) + sin ( 2x ) sin ( 3x )
=
sin ( 2x ) sin ( x )
2sin ( 3x ) cos ( x )
=
2sin ( x ) cos ( x )
sin ( 3x )
=
sin ( x )

15. HW #6
Quiz Tomorrow!!
As you think, so shall you become.
Bruce Lee