Simple trig question (1 Viewer)

[almost done now]

This is from Question 2, 2004 HSC

Could someone explain how to do it please?

Cheers.

 

[pLuvia]

d(i) You need to know the auxiliary method
A=sqrt{8²+6²}
@=tan^-1(6/8)

(ii) Using that answer you obtained in part (i) since that answer is the same as 8cosx+6sinx, then that auxlilary answer you obtained is equal to 5 then solve it you would normally do

 

[almost done now]

so that rule is just something you have to remember?

 

[Lukas1]

Ya - every time you get something with sinx and cosx in the same equation, use the AAM to get the equation into just one trig function, then solve it like any other trig thing with base angles etc.

They will usually ask you to "express in the form Rsin(x+a) or something similar. That's the AAM. Because it's an identity you can equate coefficients etc to find R and a.

 

[almost done now]

Thanks, I'll have to practise that one a bit.

Good luck on Wednesday everyone!