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Using the addition formula for sin(x+y), find sin(3x) in terms of sin(x) and hence show that sin(10) is a root of the equation 8x^3 - 6x + 1

First we state the formula for sin(x+y) sin(x+y) = sin(x)cos(y) + cos(x)sin(y) Letting y = 2x sin(x+2x) = sin(x)cos(2x) + cos(x)sin(2x) Now sin(2x) = 2sin(x)cos(x) and cos(2x) = 1 - 2sin^2(x), substitute the...
KR
Answered by Kyle R. • Maths tutor
22903 Views

Using Integration by Parts, find the indefinite integral of ln(x), and hence show that the integral of ln(x) between 2 and 4 is ln(a) - b where a and b are to be found

Using integration by parts, we can re-write the integral of ln(x) as (x ln(x) - int(x (1/x))) = x*ln(x) - x Therefore, evaluating between 2 and 4 gives us (4 ln(4) - 4) - (2 ln(2) - 2) = 2ln(16/2) - 4 + 2 = ...
KR
Answered by Kyle R. • Maths tutor
4276 Views

Why is centripetal acceleration directed inwards to the centre of the circle during centripetal motion? If I’m in a car while it’s cornering, I seem to be pushed outwards away from the centre, not inwards.

When I initially met this problem, I was slightly confused because of the car analogy above. So the way to think about this is that your body and the car are separate, and just as the car starts going around...
RG
Answered by Rudolfs G. • Physics tutor
5563 Views

Why are UK government gilt (bond) yields rising and why is that bad?

A bond or a gilt is a way of borrowing money for corporations or governments. For example, if an imaginary government wanted to borrow $100, it could issue a single bond, and an investor could buy that bond ...
RG
Answered by Rudolfs G. • Economics tutor
27150 Views

Explain the formation of a waterfall

As water flows over underlying rocks, it erodes softer rock much faster than harder rock. This creates a small step in the stream or river. Explaining the formation of waterfalls As water flows over underlyi...
EL
Answered by Ellen L. • Geography tutor
47101 Views