Express 2cos(x) + 5sin(x) in the form Rsin(x + a) where 0<a<90

Expanding Rsin(x + a): Rsin(x + a) = Rsin(x)cos(a) + Rcos(x)sin(a) Comparing coefficients of sin(x), cos(x) with first expression leads to: Rsin(a) = 2, Rcos(a) = 5 Dividing these equations gives: tan(a) = 2/5 therfore a = arctan(2/5) Squaring and adding these equations gives: R^2(sin^2(a) + cos^2(a)) = 2^2 + 5^2 therefore R = root(29)

Answered by Dan H. Maths tutor

10340 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

When do I use the chain rule and when do I use the product rule in differentiation?


How do I know which SUVAT equation to use?


Integrate lnx


How do I find a stationary point on a curve and work out if it is a maximum or minimum point?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences