Express 4sinx + 3cosx in the form Rcos(x-a)

From the following identity, cos(a-b) = cosacosb+ sinasinb, we find that 4sinx+3cosx = R(cosxcosa+sinxsina). We now equate the coefficients: 3 = Rcosa and 4=Rsina. Using basic trigonometry, we can make this into a right angled triangle, the side of length 4 being opposite to the angle a, and the side of length 3 being adjacent. The hypotenuse is therefore R, and can be calculated using Pythagoras theorem to give 5. Angle a can also be calculated, as tana = 4/3, hence a = 53.1 degrees. Therefore our answer is 5cos(x-53.1)

DT
Answered by Dorothy T. Maths tutor

19716 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the coordinates of the maximum stationary point of the y = x^2 +4x curve.


Integrate x*(5e^x)


When you integrate a function why do you add a constant?


How do I maximise/minimise a given function f(x)?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences