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Integrate (sin(x))^6 - Further mathematics (De Moivre's theorem)

Recall that sin(x) = (e ix -e -ix )/(2i) and we can rewrite the integrand as {(e ix -e -ix )/(2i)} 6 Factor out {1/(2i)} 6 , which is -1/64, of the integrand (just to make algebra easier)Use binomial expansi...
AP
Answered by Akaash P. • Maths tutor
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What are the external angles of a regular hexagon?

(A diagram would be used to show what the external angles are)For any regular shape the external angles add up to 360 degrees. The external angles will all be equal since we are dealing with a regular shape....
HB
Answered by Hannah B. • Maths tutor
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Consider the functions f and g where f(x)=3x-5 and g(x)=x-2. (a) Find the inverse function for f. (b) Given that the inverse of g is x+2, find (g-1 o f)(x).

(a) In order to find the inverse of a function, it is easiest to swap x and y and solve for y. Here this would give, x=3y-5 => x+5=3y => (x+5)/3=y. Hence, f-1(x)=(x+5)/3. (b) Here it is important to re...
RM
Answered by Rebecca M. • Maths tutor
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Solve the equations y = x + 1 and y = x^2 - 3x + 4 simultaneously.

The first step is to identify that the first equation is linear and the second equation is a quadratic as indicated by the x squared term. Next, take the first linear equation and substitute for y in the sec...
EI
Answered by Emily I. • Maths tutor
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If the area of a sector of a circle is 3*pi cm^2 and the circle has a radius of 6cm, what is the angle of the sector?

The total area of the circle is pi*r^2 = 36 piThis means that the sector is 1/12th of a circle.A circle has 360 degrees and so the angle of the sector wil be 360/12 = 30 degrees.
CA
Answered by Cameron A. • Maths tutor
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