How do I find all the solutions to sin4x=cos3x, [0, 2pi[ ?

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- Feb 11th 2008, 12:19 PMweasley74sin4x=cos3x
How do I find all the solutions to sin4x=cos3x, [0, 2pi[ ?

- Feb 11th 2008, 06:39 PMSoroban
Hello, weasley74!

Quote:

Find solutions to: .

Code:`*`

* *

* 3x*

c * *

* * a

* *

* 4x *

* * * * * * * *

b

We see that: .

. . and that and are*complementary.*

In general: .

Therefore: .

- Feb 12th 2008, 11:29 PMmr fantastic
- Feb 12th 2008, 11:41 PMmr fantastic
Another way of doing the question (which is how I picked up the missing solution):

Since (supplementary angle formula), the equation can be re-written as: .

Case 1: (where n = -m) and you have the solutions given by Soroban. Note that these solutions include .

Case 2: Since it can also be said that

.