Trig (1 Viewer)

[Psychosomatical]

"show that x = pie/3 is a solution of sin x = 1/2tan x"


How do we get full marks from this question...?

Like you can just sub in x.. then what?

 

[Timothy.Siu]

"show that x = pie/3 is a solution of sin x = 1/2tan x"


How do we get full marks from this question...?

Like you can just sub in x.. then what?

yeah u can prolly just sub it in.
just say LHS= sin pi/3=root3/2

RHS=0.5 tan pi/3=root3/2=LHS

 

[Studentleader]

"show that x = pie/3 is a solution of sin x = 1/2tan x"


How do we get full marks from this question...?

Like you can just sub in x.. then what?

sin x = tanx/2

=sinx/2cosx
​

2cosx = 1
cosx = 1/2 (At this stage you probably can do something with cosx = adj/hyp)
x = cos^-1(1/2)
x = pi/3

 

[Timothy.Siu]

sin x = tanx/2

=sinx/2cosx
​

2cosx = 1
cosx = 1/2 (At this stage you probably can do something with cosx = adj/hyp)
x = cos^-1(1/2)
x = pi/3

u have to be careful doing that, because you just cancelled out a solution...which is a no no. You were just lucky in this case.
sinx=tanx/2
2sinx=tanx
2sinxcosx=sinx
sinx(2cosx-1)=0

 

[Studentleader]

u have to be careful doing that, because you just cancelled out a solution...which is a no no. You were just lucky in this case.
sinx=tanx/2
2sinx=tanx
2sinxcosx=sinx
sinx(2cosx-1)=0

That was quite careless considering how much not cancelling too much was emphasised when I did this in year 11.

Don't know how I ended up doing that then since I'm always worried about these sorts of things - especially with changing denominators of limits.