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Express 5cosx - 3sinx in the form Rcos(x+a).

cos(x+a)=cosxcosa-sinxsina so cosa=5 sina=3 which means tana=3/5 a=0.54 RADIANS R=sqrt(5 2 +3 2 ). =sqrt(34) so sqrt(34)cos(x+0.54)
EH
Answered by Elizabeth H. • Maths tutor
16495 Views

Differentiate sin(5x) and 3cos(x) and 3tan(5x)

sin cos -sin -cos (down is differentiate and up is integrate) so, y = sin5x dy/dx = 5cos5x y=3cox dy/dx = -3sinx y=3tan5x dy/dx = 15sec 2 (5x) (remember sec(x) is the reciprocal of cos(x))
AC
Answered by Abi C. • Maths tutor
5200 Views

Find where the curve 2x^2 + xy + y^2 = 14 has stationary points

d/dx (xy) = x dy/dx + y d/dx (y^2) = 2y dy/dx [This is from the chain rule] So, d/dx (2x^2 + xy + y^2 = 14) => 4x + x dy/dx + y + 2y dy/dx = 0 set dy/dx = 0 as stationary point has gradient 0 Obtains 4x+y...
MH
Answered by Matthew H. • Maths tutor
9092 Views

Using complex numbers, derive the trigonometric identities for cos(2θ) and sin(2θ).

When dealing with complex numbers and trigonometric functions, always turn to DeMoivre's Theorem that states [cos(θ)+isin(θ)] n = [cos(nθ)+ i sin(nθ)]. If we set n=2, the we see a combination of cos(2θ) and ...
TK
Answered by Thomas K. • Maths tutor
9429 Views

Integrate (x+3)^(1/2) .dx

[whiteboard feature does not seam to be working here] Here we need to make a U sibstitution. So we take (x+3) and make this equal U so we now have the integral of u^1/2 . dx In order to switch to .du and do ...
CZ
Answered by Callum Z. • Maths tutor
5108 Views