Write 5cos(theta) – 2sin(theta) in the form Rcos(theta + alpha), where R and alpha are constants, R > 0 and 0 <=alpha < 2 π Give the exact value of R and give the value of alpha in radians to 3 decimal places.
Use the formula cos(A+B)=cosAcosB-sinAsinB, Rcos(theta+alpha)=Rcos(alpha)cos(theta)-Rsin(alpha)sin(theta)5=Rcos(alpha)2=Rsin(alpha)tan(alpha)=2/5alpha= 0.381R=sqrt(5^2+2^2)=sqrt(29)So, 5cos(theta) – 2sin(theta) = sqrt(29)cos(theta+0.381)
JW
Related Maths A Level answers
All answers ▸A curve is defined by the parametric equations x=t^2/2 +1, y=4/t -1. Find the gradient of the curve when t =2.
Express 5cosx - 3sinx in the form Rcos(x+a).
The curve C is defined by x^3 – (4x^2 )y = 2y^3 – 3x – 2. Find the value of dy/dx at the point (3, 1).
Please explain Pythgoras Theorem