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Show that: [sin(2a)] / [1+cos(2a)] = tan(a)

We start by expanding out the double trigonometric terms (sin(2a)) using the double angle formula, giving us: [2sin(a)cos(a)] / [1+cos^2(a) - sin^2(a)]. Next we spot that on the denominator (bottom half of f...
GH
Answered by George H. • Maths tutor
10196 Views

What does it mean when I get a negative value when I do a definite integral?

The definite integral gives the value of the area bounded between the curve at the given limits, and the x-axis (if we are integrating with respect to x!) If this value is negative, it means that the area un...
CL
Answered by Callum L. • Maths tutor
17830 Views

Callum mixes a drink such that the Fruit Juice and Water is a ratio of 1:4 respectively. Calculate how much of both the Fruit Juice and the Water Callum will need in order to make 2 litres of juice. (Water: ____ml, Fruit Juice: ____ml )

A ratio of 1:4 means there are 5 parts to the mixture. 2 litres of drink divided into 5 parts means there are 400 ml per part (2000ml/5 parts). As Fruit Juice has 1 part, Callum would need 400ml. As Water ha...
CM
Answered by Charlotte M. • Maths tutor
24892 Views

Differentiate y=x^2cos(x)

using the product rule product rule is dy/dx=v.du/dx+u.dv/dx let u = x^2 and v = cos(x) du/dx=2x dv/dx = -sin(x) so dy/dx=2xcos(x)-x^2sin(x)
EM
Answered by Ellen M. • Maths tutor
7684 Views

what is half of five-eights as a percentage?

(1/2)x(5/8)=5/16 100/16=6.25 6.25 x 5 = 31.25
DM
Answered by Devshi M. • Maths tutor
4095 Views