Urgent Help! (1 Viewer)

[nimrod_dookie]

The function given is:
y=cosec(x/2)-b (0<x<2П), (0<y<5)<Y<5)<Y<5)< font>

1. Find a and b given that the points (П/3, 2) and (П,0) are on the curve and substitute them into the model function.

I need help with this urgently. Please. Any assistance would be greatly appreciated.

 

[SoulSearcher]

Umm, where's a?

 

[nimrod_dookie]

Oh shit! Sorry. Its y=acosec(x/2)-b

 

[SoulSearcher]

Ok, y = acosec(x/2) - b
Point (pi/3, 2)
2 = acosec(pi/6) - b
2 = 2a - b ............... (1) , because cosec(pi/6) = 2
Point (pi/0)
0 = acosec(pi/2) - b
0 = a - b, as cosec(pi/2) = 1
Therefore a = b ............ (2)
Substitute into (1) above,
2 = 2a - a
a = 2
Using (2), a = b
.'. b = 2
Therefore function is y = 2cosec(x/2) - 2

 

[nimrod_dookie]

Thankyou so much Soul.

 

[nimrod_dookie]

How would you go about showing the function y=2cosec(x/2)-2 is symmetric about x=pi.

The hint is to use f(pi+x)=f(pi-x) for symmetry about x=pi.

There is nothing in the textbooks/notes I use on this specific aspect.

 

[pLuvia]

Given f(pi+x)=f(pi-x)
Sub in pi+x and pi-x into the equation and you should see both of them should equal each other hence it is symmetrical about x=pi

 

[nimrod_dookie]

Thankyou