## ChristopherW28 2 years ago How do you factor sin^3x + cos^3x?

1. myininaya

Do you know how to factor a sum of cubes?

2. myininaya

There is a cute formula for it.

3. myininaya

$a^3+b^3=(a+b)(a^2-ab+b^2)$

4. ChristopherW28

Looks cute lol thank you

5. myininaya

lol. Do you know how to use it with the trig functions?

6. myininaya

$(\sin(x))^3+(\cos(x))^3=a^3+b^3$

7. myininaya

should be easy for you to determine what is a and what is b.

8. myininaya

if it isn't then let me know so i can explain further

9. ChristopherW28

I've got the equation down but what to do first?

10. ChristopherW28

Do I multiply what's in the parenthesis?

11. myininaya

no

12. myininaya

tell me what a is and what b is based on what I wrote above

13. ChristopherW28

A is sin and b is cos

14. myininaya

$(\sin(x))^3+(\cos(x))^3=a^3+b^3$

15. myininaya

ok so just go to the other side of the formula and replace a with sin(x) and replace b with cos(x) and then you are done don't do nothing more

16. ChristopherW28

I did :)

17. myininaya

ok then you are done sir

18. myininaya

$a^3+b^3=(a+b)(a^2-ab+b^2)$ everywhere we seen an a we put sin(x) everywhere we seen a b we put cos(x)

19. ChristopherW28

Thanks!

20. myininaya

np :)

21. ChristopherW28

I will have another question in a moment

22. myininaya

k