How many solutions to? (1 Viewer)

[lookoutastroboy]

Well, how many solutions are there to sin x = cos 2x between 0 and 2pi - some ppl are saying 3 and some ppl are sayin 4 in my class?

 

[hscishard]

I found 3. Not sure where the other one came from

 

[lilvietboi93]

do u go 2 mce?

 

[mirakon]

Well, how many solutions are there to sin x = cos 2x between 0 and 2pi - some ppl are saying 3 and some ppl are sayin 4 in my class?

sinx= cos 2x

sinx=cos^2 x-sin^2 x

2sin^2 x +sinx -1=0

(2sinx-1)(sinx+1)=0

Therefore solutions are sinx=0.5 (2 solutions from 0 to 2pi) and sinx=-1 (1 solution between 0 to 2pi)

Solutions are pi/6, 5pi/6, 3pi/2

Q.E.D

 

[fullonoob]

+1 to mirakon
observe the graph of sinx and you will see it has a local min at -1, and this only occurs once within a period of 2pi