Express 3cosx-4sinx in the form Rcos(x+a) for some R>0 and 0<a<90 giving the value of a correct to the nearest minute

Hence solve the equation 3cosx-4sinx=5 for in the domain of [0,360]

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- Sep 12th 2009, 04:58 PMrequaltricky trig equations
Express 3cosx-4sinx in the form Rcos(x+a) for some R>0 and 0<a<90 giving the value of a correct to the nearest minute

Hence solve the equation 3cosx-4sinx=5 for in the domain of [0,360] - Sep 12th 2009, 07:25 PMsongoku
Hi requal

I'm not sure what you mean by "nearest minute". Maybe it means nearest degree?

Let :

p cos x - q sin x = R cos (x+a)

$\displaystyle R=\sqrt{p^2+q^2}$

Then, expand RHS and compare it with LHS to find cos(a) and sin(a). Hence, find a :) - Sep 12th 2009, 09:50 PMmr fantastic
- Sep 13th 2009, 03:00 AMsongoku
Hi mr fantastic

Oh I see. Find (a) in degree first then convert it to minute.

Thanks - Sep 14th 2009, 01:57 AMrequal
sorry, to bump but I'm still confused. Why does R equal the square root of p^2+q^2

- Sep 14th 2009, 03:13 AMsongoku
Hi requal

p cos x - q sin x = R cos (x+a)

p cos x - q sin x = R cos(x) cos(a) - R sin(x) sin(a)

Comparing coefficient :

p cos x = R cos(x) cos(a)

p = R cos(a) .........................(1)

q sin x = R sin(x) sin(a)

q = R sin(a)...........................(2)

Square (1) and (2) and add them :

p^2 = R^2 [cos(a)]^2

q^2 = R^2 [sin(a)]^2

--------------------------- +

p^2 + q^2 = R^2