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A right angled triangle has two smaller sides length 3 and 4, what is the length of its longest side?

As we are told it is a right angled triangle we known that we can use Pythagoras's formula of c 2 = a 2 +b 2 given that we have been given lengths of 3 and 4 we simply substitute these into the equation c 2 ...
BG
Answered by Benjamin G. • Maths tutor
3502 Views

Integrate sin^2(x) with respect to x

use trigonometric identities i.e. Cos(2x) = Cos 2 (x) - Sin 2 (x) (a) Cos 2 (x) + Sin 2 (x) = 1 (b) Therefore: Cos 2 (x) = 1 - Sin 2 (x) (c) Combining (a) and (c) we achieve Cos(2x) = 1 - 2 Sin 2 (x) Rearran...
OL
Answered by Oscar L. • Maths tutor
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Given that 2cos(x+50)°=sin(x+40)° show tan x° = tan 40°/3

The formulae for the sum the sine and cosine of two angles are: 2(cos x°cos 50°- sin x°sin 50°)= sin x°cos 40°+cos x°sin 40°cos 50°= sin 40°sin 50° = cos 40° Therefore, 2 cos x°sin 40°- 2 sin x°cos 40° = sin...
PT
Answered by Prashasti T. • Maths tutor
8258 Views

Integrate x * sin(x) with respect to x by using integration by parts

The general formula for integration by parts to integrate something of the form u * v' is: u * v - (integral)[ (u' * v) dx ] . Thus we first need to write x * sin(x) in the form u * v' . Lets pick u = x and ...
JW
Answered by Jamie W. • Maths tutor
6124 Views

write 2(sin^2(x)- cos^2(x)) + 6 sin(x) cos(x) in terms of cos(2x) and sin(2x)

We use the following double angle formulae cos(2x) = cos^2(x) - sin^2 (x) and sin(2x) = 2sin(x)cos(x) to see that 2(sin^2(x)- cos^2(x)) + 6 sin(x) cos(x) = -2-(sin^2(x)+ cos^2(x)) + 3*2 sin(x) cos(x) = -2cos...
NR
Answered by Nicola R. • Maths tutor
5986 Views