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Express asin(x) + bcos(x) in the form Rsin(x+c), where c is a non-zero constant.

The trick to solving this is to use the trig identity sin(a+b) = sin(a)cos(b) + sin(b)cos(a) From the identity above, we can write rewrite Rsin(x+c) as follows: Rsin(x+c) = R[sin(x)cos(c) + sin(c)cos(x)] Exp...
LH
Answered by Louis H. • Maths tutor
7933 Views

Integral of a compound equation (or otherwise finding the area under a graph): f(x) = 10x*(x^(0.5) - 2)

This can be done 'by parts' or by expanding. In this case it would be easier to expand as it is possible to deal with terms individually here. This becomes: 10x x 1/2 - 10x 2 = 10x 3/2 - 20x We know this bec...
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Answered by Roden D. • Maths tutor
4282 Views

By forming and solving a quadratic equation, solve the equation 5*cosec(x) + cosec^2(x) = 2 - cot^2(x) in the interval 0<x<2*pi, giving the values of x in radians to three significant figures.

To solve the equation given in the question, we must first express the given equation in terms of only one trigonometric function, i.e. either all in cosec or all in cot. The easiest route would be cosec, si...
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Answered by Nadia M. • Maths tutor
9749 Views

Can I have help with integrating by parts? I am unsure on how to use the formula.

Integrating by parts is simple. Simply put the equation into two parts, U and dV/dx. When considering which part of the original function will be U and which part will take dV/dx, you should consider which p...
ML
Answered by Milo L. • Maths tutor
3711 Views

A ball is thrown from ground level at an angle of 30 degrees from the horizontal with a velocity of 20 m/s. It just clears a wall with a height of 5m, from this calculate the distances that the wall could be from the starting position.

The first thing to do is draw a diagram to visualise the problem. Next we write down all the information the question gives us as well as which values we want to find. For this question it would be S=5m, U=2...
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Answered by Aysha A. • Maths tutor
4691 Views