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How do I write the function 3cosθ+4sinθ in the form Rsin(θ + α), where R and α are positive constants?

Split it up into steps: Step 1: Use compound angle trigonometric formula to re-write Rsin(θ + α) Since generally sin(θ ± φ) = sinθcosφ ± cosθsinφ Rsin(θ + α) = R(sinθcosα + cosθsinα) = Rsinθcosα + Rcosθsinα ...
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Answered by Oliver G. • Maths tutor
12942 Views

Calculate the distance of the centre of mass from AB and ALIH of the uniform lamina.

The diagram shows the lamina shape. To begin, divide the lamina into smaller sections and calculate the area. In this example, the lamina is best divided into sections A, B and C. Calculate the areas. For ex...
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Answered by Chandler S. • Maths tutor
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How do you factorise the following quadratic: x^2 - 5*x - 14?

An example of an application of factorising quadratics is to find the unknown in the equation, x. Factorising means writing the above equation in the form (x+a)(x+b)=0 Using FOIL (First, Outer, Inner, Last) ...
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Answered by Emma P. • Maths tutor
4265 Views

Solve x^4+2x^2-3=0

The trick with this question is noticing the hidden quadratic as quartic equations are unsolvable at A-level. Letting u=x^2 the question becomes u^2+2u-3=0 which most students would be able to solve. To fact...
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Answered by Ben S. • Maths tutor
7737 Views

How to solve simultaneous equations with a quadratic

Example. " Solve the simultaneous equations y + 4x + 1 = 0 y^2 + 5x^2 + 2x = 0 " We can rearrange the first equation to something that we can substitute into the second equation, for example y = -4...
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Answered by Tilly W. • Maths tutor
3697 Views