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There are 11 pens in a bag, 4 Green and 7 Blue. What is the probability of picking the same coloured pens?

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LH
Answered by Laura H. • Maths tutor
4744 Views

Express '6cos(2x) +sin(x)' in terms of sin(x).

6cos(2x) +sin(x).Using the double angle formula for cosine (or otherwise), cos(2x) = cos(x)cos(x) - sin(x)sin(x) .cos(2x) = cos^2(x) - sin^2(x) .Hence, 6cos(2x) +sin(x) = 6(cos^2(x) - sin^2(x)) + sin(x). Now...
RM
Answered by Robbie M. • Maths tutor
5937 Views

Find the x and y coordinates of the turning points of the curve 'y = x^3 - 3x^2 +4'. Identify each turning point as either a maximum or a minimum.

The first part of the problem is solved by differentiating once and equating this to zero: y = x^3 - 3x^2 +4 . dy/dx = 3x^2 - 6x . dy/dx = x(3x - 6) . At the turning points; x(3x - 6) = 0 (turning points occ...
RM
Answered by Robbie M. • Maths tutor
13768 Views

Calculate the derivative of the following function: f(x)=cos(3x))^2

The answer can be found by using the chain rule and simple substitution as well as basic knowledge of differentiation.f’(x)= -6cos(3x)sin(3x)
JM
Answered by Jeff M. • Maths tutor
5297 Views

What are the most important trig identities we need to know?

cos^2(A) + sin^2(A) = 1, sin(A+B) = sinAcosB + cosAsinB, cos(A+B) = cosAcosB - sinAsinB, sin2A = 2sinAcosA (if A = B), cos2A = cos^2(A) - sin^2(A) (if A = B), cos2A = 1 - 2sin^2(A) => sin^2(A) = 1/2(1 - c...
BH
Answered by Bowen H. • Maths tutor
4656 Views