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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.)

R²

Answered by Prashan B. • Maths tutor

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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) ...

Answered by Aphisha S. • Maths tutor

3377 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 t...

Answered by Ruth D. • Maths tutor

3508 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 = r² where the centre = (a,b) and the radius = r

Thus using the equation above we can conclude that the centre is (2,-5)

...

Answered by Michael C. • Maths tutor

4974 Views

The curve y = 4x^2 + a/ x + 5 has a stationary point. Find the value of the positive constant a given that y-ordinate of the stationary point is 32.

This question might look hard but can be easily answered by breaking it down into steps and remembering a few key things. The first step is to recognise that the question is mentioning a stationary point ...

Answered by Helen B. • Maths tutor

10621 Views