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How do you calculate the derivative of cos inverse x?

When differentiating cos inverse x, the typical method is to make y equal to cos inverse x.By taking cos of both sides: x = cosy.You can then differentiate with respect to y, obtaining that: (dx/dy) = - siny...
WW
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How do you integrate (sinx)^2?

(sinx)^2 (similarly to (cosx)^2) cannot be integrated in this form. There is a standard method to get past this though, which makes use of the cos double angle formula:cos(2x) = (cosx)^2 - (sinx)^2 = 1 - (si...
WW
Answered by Will W. • Maths tutor
43712 Views

How would I resolve forces on a slope?

First pick a set of axis to use. This would be in the directions of which the majority of the forces follow. With the forces which are at angles to the majority of the forces, create a triangle of the horzio...
GB
Answered by George B. • Physics tutor
3563 Views

Derive from the standard quadratic equation, the form of the quadratic solution

ax 2 +bx+c=0 : basic quadratic equation a(x 2 + bx/a) + c=0 a((x+b/2a) 2 - b 2 /4a 2 ) + c=0 (retain equation with only one x variable; compensate for b term squared out with term - b 2 /4a 2, ) a(x+b/2a) 2 ...
JD
Answered by Jaiveer D. • Maths tutor
6968 Views

Write tan(3x) in terms of tan(x). Hence show that the roots of t^3 - 3t^2 - 3t + 1 = 0 are tan(pi/12), tan(5pi/12) and tan(3pi/4)

The first part is relatively simple. If we write tan(3x) as tan(2x+x) we can use addition formulae to give: tan(2x+x)= (tan(2x)+tan(x))/(1-tan(2x)tan(x)) tan(2x) = 2tan(x)/(1-tan^2(x)) Substituing this in an...
DG
Answered by Daniel G. • Maths tutor
54090 Views