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# C3 Question watch

1. Hi I have a question that I need explaining please
The question is

a) Express 3cosx + 4sinx in the form Rcos(x-a) where R>0 and 0<a<90
b) Hence find the maximum value of 3cosx + 4sinx and the smallest positive value of x for which this maximum occurs.

I understand a). The answer is R = 5, a = 53.1
but I do not get b)
The unofficial mark scheme says max 5 when x = 53.13 where cos0 = 1

2. (Original post by Ram92)
Hi I have a question that I need explaining please
The question is

a) Express 3cosx + 4sinx in the form Rcos(x-a) where R>0 and 0<a<90
b) Hence find the maximum value of 3cosx + 4sinx and the smallest positive value of x for which this maximum occurs.

I understand a). The answer is R = 5, a = 53.1
but I do not get b)
The unofficial mark scheme says max 5 when x = 53.13 where cos0 = 1

The maximum value of cos theta or sin theta is one. In this case you have 5 cos theta. So maximum is 5
3. Well you have the equation 5cos(x-53.1)

What value of x do you have to sub in to get the maximum possible value?
4. so the maximum value of 3cosx + 4sinx will be the same as the maximum value of 5cos(x-53.1)

the maximum of cosx is 1, and the smallest positive value of x where cosx = 1 is 0. so equate x-53.1 to 0 to find that x = 53.1
5. (Original post by Ram92)
Hi I have a question that I need explaining please
The question is

a) Express 3cosx + 4sinx in the form Rcos(x-a) where R>0 and 0<a<90
b) Hence find the maximum value of 3cosx + 4sinx and the smallest positive value of x for which this maximum occurs.

I understand a). The answer is R = 5, a = 53.1
but I do not get b)
The unofficial mark scheme says max 5 when x = 53.13 where cos0 = 1

The maximum point of a cos graph is cos(0). So x - 53.1=0,
which means x=53.1

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