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What is De Moivre's theorem?

De Moivres theorem states that e^j(theta) = cos (theta) +jsin (theta) and this can be used to convert powered trig functions to the form of regular sines and cosines (i.e. sin^3(x) into a sum of terms includ...
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Answered by Kieran T. • Maths tutor
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Given that y = sin(2x)(4x+1)^3, find dy/dx

The product rule states that (uv)' = u'v + uv' Therefore we know that to find dy/dx we must have (sin(2x))'(4x+1)^3 +sin(2x)((4x+1)^3)' We can differentiate sin(2x) to 2cos(2x) and using the chain rule we ca...
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Answered by Myles M. • Maths tutor
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When do we use the quadratic formula, and when the completing the square method?

First, you have to understand that both are essentially the same; the formula is based on the completing the square method. ax^2+b^x+c=0 can with appropriate steps be transformed to x = (-b +- root(b^2-4ac))...
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Answered by Ioannis P. • Maths tutor
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How do you rationalise the denominator?

If a denominator is has just one square root (i.e 1/(3)^0.5). Then, since it is a fraction you can multiply top and bottom by the same number and maintain the value of the fraction. Hence we multiply top and...
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Answered by Natasha A. • Maths tutor
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Write down the values of (1) loga(a) and (2) loga(a^3) [(1) log base a, of a (2) log base a of (a^3)]

Let's first go to the whiteboard where I will explain what a logarithm is. The equation, loga(b) = x, could be re-written into the form, a^x = b. This is true for all logarithmic equations. There is a rule f...
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Answered by Sohail H. • Maths tutor
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