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Express cos(2x) in terms of acos^2(x) + b

cos(2x)=cos 2 (x) - sin 2 (x)use sin 2 (x) = 1 - cos 2 (x)so cos(2x)=cos 2 (x) - (1 - cos 2 (x))cos(2x)=2cos 2 (x) - 1so a = 2 and b = -1
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Given that f(x) = x^2 (3x - 1)^(1/2) find f'(x)

This is an example of a question using the product rulelet u = x 2 and v = (3x - 1) 1/2 then u' = 2x and v' = 3 X 1/2 (3x - 1) -1/2 using the product rule we get f'(x) = x 2 X 3/2 (3x - 1) -1/2 + (3x - 1) 1/...
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How do I know when to use sine, cos or tan when working with right angled triangles?

When dealing with right angled triangles, you just need to remember 'SOHCAHTOA'. If you struggle to remember this, you may find it easier to recall:' S ome O f H er C hildren A re H aving T rouble O ver A lg...
JG
Answered by Jonny G. • Maths tutor
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A curve has equation y = x^3 - 48x. The point A on the curve has x coordinate -4. The point B on the curve has x coordinate - 4 + h. Show that that the gradient of the line AB is h^2 - 12h.

First, let's recall the gradient formula:grad = change in y / change in x = y2 -y1 / x2 - x1So let's label point A as x1, and point B as x2, and find the corresponding y1 and y2 using the equation of the cur...
OW
Answered by Oliver W. • Maths tutor
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Plot the graph for y = 4x - 3

Create a table for x and y x,1,2,3y,1,5,9Draw the line on a graph
CS
Answered by Conor S. • Maths tutor
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