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How do I derive the indefinite integral of sine?

The integral of sine is pretty easy to remember as it is -cos + C. However you need to be able to prove this, without using the integral of cosine. This method uses sines exponential form. As e iθ​ = cosθ + ...
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Answered by Lucile C. • Maths tutor
3110 Views

Solve the equation (2 cos x) = (sin 2 x) , for 0 ≤ x ≤ 3π .

cos x = 0, sin x = 1, solved using trigonometric identities. 3(pi) means 3/2 times round a the circle, therefore using graphs answer is pi/2, 3(pi/2), 5(pi/2)
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Answered by Dhruv C. • Maths tutor
6705 Views

Factorise z^3+1 into a linear and quadratic factor. Let y=(1+i√3)/2. Show that y is a cube root of -1. Show that y^2=y-1. Find the value of (1-y)^6.

To factorise z 3 +1 into a linear and quadratic factor, it is best to try the factor theorem first. We set the equation to zero: z 3 +1=0.We need to find a value of z such that the above is true. By inspecti...
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Answered by Henry L. • Maths tutor
24925 Views

Take the square root of 2i

As with much of complex number the trick here is to change forms to polar representation.If you think of an argand diagram the number i will be represented as a point straight up on the imaginary axis a dist...
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Answered by Simon T. • Maths tutor
7893 Views

The quadratic equation 2x^2-8x+1 = 0 has roots a and b. Find the value of a + b and ab

There is no need to solve the quadratic equation here. Use the formulae for the sum and product of roots where: a+b = -b/a and ab = c/a Therefore in this instance: a+b = -(-8)/2 = 4 and ab = 1/2
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Answered by Alok K. • Maths tutor
9536 Views