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Consider a sin graph and all the points on the graph which are equal to 0.5. You'll find that, between one period of a positive sin graph, invsin(0.5) may equal 30 degrees or 150 degrees. The equation can no...

Differentiation is a way of measuring a rate of change. Formally, we can look at two points on a curve and as an example, I would use the x^2 curve. We can plot on a point (x,x^2) and a point (x+h, (x+h)^2)....

Let A=7x and B=3x( From the formulae we know that sinxcosx= 1/2(sin(A+B)+sin(A-B))So if we replace A=7x and B=3x in this equation: 1/2(sin(7x+3x)+sin(7x-3x))= = 1/2 (sin(10x)+sin(4x))Now we just integrate 1/...

Let u=6x-3 , then y=u^-0.5hence, du/dx=6 and dy/du= -0.5u^-3/2then, as dy/dx =dy/du * du/dx dy/dx=(-0.5u^-3/2 )*6= -3(6x-3)^-3/2substitute x=2 to give the required value required value : -1/9

RHS should always be 0 so start by taking that across.Now we want two numbers, they need to add up to make - 5 and multiply to make -14.Solve for this and we get -7 and +2.Use this information to factorise: ...