## TNNG 2 years ago Find all solutions to the equation. cos x = sin x

1. T0mmy

Doesn't make sense

2. mathmate

When in doubt, draw a sketch: |dw:1357770541986:dw| The sketch is for 0<=x <=2pi. The general solution requires the form x=.... +2k pi where k is an integer.

3. TNNG

still do not get it

4. mathmate

You will need to solve for sin(x)=cos(x) between 0 and 2pi. The same solution will be valid if you add 2k pi to the obtained solution. Are you able to find the solution between 0 and 2pi?

5. TNNG

look is the answer pi/2 +n(pi)(0,+/-1,+/- 2

6. BluFoot

Looking at the unit circle is another way to do it if you've learned that. When are the cos and sin values identical?

7. TNNG

8. cinar

|dw:1357780533732:dw|

9. TNNG

so it is pi/2 + n(pi)

10. cinar
11. cinar

yes one solution is that..

12. TNNG

ok thank you i think i get it now

13. cinar

I meant pi/4+2npi

14. TNNG

the other is 7pi /4 + 2npi

15. BluFoot

it should be pi/4 +2npi and 5pi/4 + 2npi

16. TNNG

i dont have a answer like that it is just pi/4 +2npi and 7pi /4 + 2npi. the answer with 5pi/4 + 2npi is paired with 3pi/4 + 2npi

17. BluFoot

I don't know what the question is exactly but the solution to sinx=cosx is definitely x=pi/4 +2npi and x=5pi/4 + 2npi

18. TNNG

Find all solutions to the equation. cos x = sin x is the question they are asking

19. BluFoot

Well then their answer is wrong!

20. mathmate

|dw:1357774360119:dw|

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