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1. (a) Express 7cosx - 24sin x in the form R cos (x + a), (b) hence what is the minimum value of this equation

(a) Rcos (x+a) = Rcosxcosa - Rsinxsina 7cosx - 24sinx = Rcosxcosa - Rsinxsina Rcosa = 7, Rsina = 24 Tan a = 24/7 a = 1.287 (3 S.F.) R 2 = 24 2 + 7 2 R = 25 Therefore 25cos(x + 1.287) (b) minimum value = -1 *...
PB
Answered by Prashan B. • Maths tutor
15370 Views

Find the normal to the curve y = x^2 at x = 5.

Differentiate the original equation (y = x^2) to find the gradient (m) of the line which is a tangent to the curve. Dy/dx = 2x Therefore m = 2 Calculate the negative reciprocal (m2) which will give the gradi...
AS
Answered by Aphisha S. • Maths tutor
4533 Views

Use the identity for sin(A+B) to find the exact value of sin 75.

From reading the question, we need to use the addition formula for sin(A+B)= sinAcosB+cosAsinB. So we need to think what are two common values for sine and cosine that we know and have exact answers for that...
RD
Answered by Ruth D. • Maths tutor
5214 Views

Find the coordinates of the centre C and the length of the diameter of a circle with the equation (x-2)^2 + (y+5)^2 = 25

Equation of a circle -> (x-a) 2 + (y-b)^2 = r 2 where the centre = (a,b) and the radius = r Thus using the equation above we can conclude that the centre is (2,-5) In order to find the diamerer fo the cir...
MC
Answered by Michael C. • Maths tutor
6256 Views

Solve 9x - 3 = 4x + 17

The objective of the question is to find an answer to x = ?, where ? is a number. Start by 'moving' all the x's to one side of the equals sign and all the numbers to the other. This can be done by adding / s...
MC
Answered by Michael C. • Maths tutor
5948 Views