• Support PF! Buy your school textbooks, materials and every day products Here!

Trigonometry expansion

  • Thread starter Panphobia
  • Start date
  • #1
435
13

Homework Statement



We know that sin(2⋅x)=2⋅sin(x)⋅cos(x)and cos(2x)=cos^2(x)−sin^2(x). Use the appropriate formula to expand cos(8x) in terms of one of these two formulas.


Homework Equations


sin(2⋅x)=2⋅sin(x)⋅cos(x)
cos(2x)=cos^2(x)−sin^2(x)

The Attempt at a Solution


I am not looking for help with the solution, I just want to know what the question is asking me to do. Is it asking me to sub cos(8x) into these equations like cos(8x) = cos^2(4x) - sin^2(4x)? If not what is it asking me to do?

Thank You!
 

Answers and Replies

  • #2
33,262
4,963

Homework Statement



We know that sin(2⋅x)=2⋅sin(x)⋅cos(x)and cos(2x)=cos^2(x)−sin^2(x). Use the appropriate formula to expand cos(8x) in terms of one of these two formulas.


Homework Equations


sin(2⋅x)=2⋅sin(x)⋅cos(x)
cos(2x)=cos^2(x)−sin^2(x)

The Attempt at a Solution


I am not looking for help with the solution, I just want to know what the question is asking me to do. Is it asking me to sub cos(8x) into these equations like cos(8x) = cos^2(4x) - sin^2(4x)?
Yes. Now do the same sort of thing on the cos(4x) and sin(4x) terms.

Note that the notation cos2(4x) means [cos(4x)]2, and similar for sin2(4x).
If not what is it asking me to do?

Thank You!
 

Related Threads on Trigonometry expansion

  • Last Post
Replies
3
Views
675
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
5
Views
810
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
12
Views
495
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
4
Views
953
  • Last Post
Replies
3
Views
903
  • Last Post
Replies
8
Views
2K
Top