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curve C with parametric equations x = 4 tan(t), y=5*3^(1/2)*sin(2t). Point P lies on C with coordinates (4*3^(1/2), 15/2). Find the exact value of dy/dx at the point P.

dy/dx = dy/dt *dt/dx (chain rule). x=4tan(t) hence dx/dt = 4 sec 2 (t) y = 5 3 1/2 sin(2t) hence y'= 10 3 1/2 cos(2t) therefore dy/dx = 10 3 1/2 cos(2t) / 4 sec 2 (t). Since P is on point with x=4 3 1/2 we c...
HP
Answered by Harry P. • Maths tutor
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Find the first derivative of r=sin(theta+sqrt[theta+1]) with respect to theta.

To find the first derivative we must apply the chain rule. Our aim is to find dr/d(theta). We start by bringing the differential of what's inside the sine brackets outside and multiplying it by the different...
TD
Answered by Tutor61926 D. • Maths tutor
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Perhaps an introduction to integration with a simple integral, e.g. the integral of x^2

I would first write out the integral with correct notation, explaining to my tutee exactly what I am drawing and why. I will then explain the 'n+1' rule for integrating simple powers. I will go through the i...
RC
Answered by Reece C. • Maths tutor
3742 Views

Find, in radians, the general solution of the equation cos(3x) = 0.5giving your answer in terms of pi

we have cos (3x) = 0.5 (1) we know that in the interval between [-pi; pi] there are two values that satify the equation cos(y) = 0.5 (2) the two solutions are y=pi/3 and y=-pi/3 in this interval. More genera...
MB
Answered by Marie B. • Maths tutor
7879 Views

(GCSE) A rectangle has the following characteristics: its length is (2x + 5), its width is (3x - 2). The perimeter of the rectangle is 46 cm. What is the value of x?

First of all draw the rectangle, name its sides and annotate its characteristics. Define the data you have and what you are looking for. Write down the general formula for the perimeter of a rectangle: p = a...
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Answered by Giulia D. • Maths tutor
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