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Show that the equation 2sin^2(x) + 3sin(x) = 2cos(2x) + 3 can be written as 6sin^2(x)+3sin(x) - 5 = 0. Hence solve for 0 < x < 360 degrees. Giving your answers to 1.d.p.

2sin^2(x) + 3sin(x) = 2cos(2x) + 32sin^2(x) + 3sin(x) = 2(cos^2(x) - sin^2(x) ) + 32sin^2(x) + 3sin(x) = 2(1- 2sin^2(x) ) + 32sin^2(x) + 3sin(x) = 2 - 4sin^2(x) + 36sin^2(x) + 3sin(x) - 5 = 0 let sin(x) =...

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Answered by Tom A. Maths tutor
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The curve C has equation y = (x^2 -4x - 2)^2. Point P lies on C and has coordinates (3,N). Find: a) the value of N. b) the equation of the tangent to C at the point P, in the form y=mx+c where m and c are constants to be found. c) determine d^2y/dx^2.

a) Sub x=3 into the given equation. N is found to be 25.b) Finding dy/dx gives me, as the first differential is the gradient.First differentiate the power and then multiply the differential of the express...

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Answered by Tom A. Maths tutor
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Two masses A and B, 2kg and 4kg respectively, are connected by a light inextensible string and passed over a smooth pulley. The system is held at rest, then released. Find the acceleration of the system and hence, find the tension in the string.

First we draw a diagram of this system (on whiteboard). Remember to label diagram correctly - the tension on both sides act towards each other.
Since B is a larger mass, we know that mass A will mov...

Answered by Maths tutor
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A,B and C all lie on the line x^2 + y^2 = 49 where A is on the y axis, B is on the X axis and C is the mid point of the straight-line connecting A and B.

As we know that A and B are on the axis so sub in X=0 and Y=0 into the equation to solve for the co-ordinates A and B.For A 02+y2=49y= square root of 49 = 7Do the same for B, whic...

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Answered by Oliver W. Maths tutor
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What is the point of a derivative?

A derivative is a rate of change. For example, let y equal some function of x. Then the derivative of y with respect to x is asking how much y changes with respect to x. We can show this for any x and if ...

Answered by Maths tutor
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