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Why is sin(t)^2 + cos(t)^2 = 1 true for all t?

To answer this we need to consider a circle of radius r centred at the origin, drawn in the x,y plane. We'll draw a right-angled triangle such that the hypotenuse is the radius, and say that the point where ...
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Answered by Matt V. • Maths tutor
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(a) Use integration by parts to find ∫ x sin(3x) dx

The question asks for integration by parts. Therefore we need to differentiate one variable and integrate the other. First we need to decide which variable is going to be which. Algebra should always be diff...
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Answered by George A. • Maths tutor
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What's the gradient of the curve y=x^3+2x^2 at the point where x=2?

Gradient is change in y divided change in x.As the change shrinks to effectively nothing (as we want to gradient at a point, not between points), we use dy/dx (the derivative of y with respect to x), to work...
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Answered by Zachary I. • Maths tutor
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Prove by induction that, for n ∈ Z⁺ , [3 , -2 ; 2 , -1]ⁿ = [2n+1 , -2n ; 2n , 1-2n]

STEP 1: Prove that the theorem holds for n = 1. Substitute n = 1 into the equation and show that the LHS = RHS. STEP 2: Assume that the relation is true when n = k. STEP 3: Prove that the relation holds for ...
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Answered by Flavia T. • Maths tutor
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A particle P of mass 2 kg is held at rest in equilibrium on a rough plan. The plane is inclined to the horizontal at an angle of 20°. Find the coefficient of friction between P and the plane.

For any mechanics question such as this one the best way to start off is by drawing a diagram of the system and including all the forces acting on the particle P. In order to do so, we have to account for th...
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Answered by Fernando B. • Maths tutor
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