OCR C3 Jun 2010 Trig

8(i) Express 3 cos x + 3 sin x in the form R cos (x-a)...

8(ii) The expression T(x) is defined by

$T(x)=\frac{8}{3cosx+3sinx}$

Find the smallest possible value of x satisfying

$T(3x)=\frac{8}{9}\sqrt{6}$

giving your answer in an exact form.

Hi guys,

My sister's stuck on a particular question on this paper, and after having a look, neither my dad nor I can see how to solve it! We've done the first part, but are having trouble with the second.



We've done this and got the right answer:

$3\sqrt{2}cos(x-\frac{\pi}{4})$

The next part says:



I understand that T(3x) isn't the same as 3(T(x)), so I used a "function machine" diagram and concluded that T(3x) = R cos (3x-a), but I get nowhere near the right answer when I try and solve it. I got about 0.61..., whereas it's pi/16. Can anyone shed any light?

Thanks a lot!

Hi guys,

My sister's stuck on a particular question on this paper, and after having a look, neither my dad nor I can see how to solve it! We've done the first part, but are having trouble with the second.



We've done this and got the right answer:

$3\sqrt{2}cos(x-\frac{\pi}{4})$

The next part says:



I understand that T(3x) isn't the same as 3(T(x)), so I used a "function machine" diagram and concluded that T(3x) = R cos (3x-a), but I get nowhere near the right answer when I try and solve it. I got about 0.61..., whereas it's pi/16. Can anyone shed any light?

Thanks a lot!

I have never heard of a "function machine" diagram in my entire life

From the previous question try writing

$T(x) = \frac{8}{3cos(x) + 3sin(x)} = \frac{8}{3\sqrt{2}cos(x - \frac{\pi}{4})}$

Then

$T(3x) = \frac{8}{3\sqrt{2}cos(3x - \frac{\pi}{4})}$

Then solve

$T(3x) = \frac{8}{3\sqrt{2}cos(3x - \frac{\pi}{4})} =\frac{8}{9}\sqrt{6}$

by rearranging and solving how you would normally for any trig function.

I'm getting pi/36 and not pi/16. ???

Sorry, just checked the mark scheme and it is pi/36.

Did you use the same method as TheIrrational?

Just realised I'm an idiot and have looked at this paper for so long I kept misreading the question. I'll work through now, but I think I see what I've done wrong. Thanks for all your help!