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Using the trigonometric identity (sinx)^2 + (cosx)^2 = 1, show that (secx)^2 = (tanx)^2 + 1 is also a trigonometric identity.

We can divide by (cosx)^2 across the identity (sinx)^2 + (cosx)^2 = 1 (which can be derived from properties of the unit circle and a bit of Pythagoras’ theorem) to achieve [(sinx)^2 / (cosx)^2] + [(cosx)^2 /...
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Answered by Annie B. • Maths tutor
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The random variable J has a Poisson distribution with mean 4. Find P(J>2)

P(J>2) = P(J=0)+P(J=1) [split it up] P(X=t)= (V^t)/t!*e^V where V=4 in this case [use the formula] P(J>2) = 4^0/0!*e^4 + 4^1/1!*e^4 =1/e^4 + 4/e^4 = 5e^-4 which is roughly 0.0916
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Answered by Nathan C. • Maths tutor
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3. The point P lies on the curve with equation y=ln(x/3) The x-coordinate of P is 3. Find an equation of the normal to the curve at the point P in the form y = ax + b, where a and b are constants.

P- (3,0) y=ln(x/3) u=x/3 y=ln(u) ​​​​​​ du = 1/3 dy = 1/u = 3 dx du dy = du x dy dx dx du = 1/3 x 3 = 1 gradient at normal = -1 equation at normal = y = m(x) + c 0 = -3 + c 3 = c Answer: equation at normal =...
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Answered by Kaushalya B. • Maths tutor
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Differentiate 3x^(2)+xy+y^(2)=12 with respect to x

this is implicit differentiation. We start by differentiating 3x^(2) to get 6x (lower the power by 1, multiply by the original power). For xy, we use the product rule, giving us y + (x)dy/dx (this is the imp...
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Answered by Noyonika L. • Maths tutor
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How do I use the product rule for derivatives?

Imagine a function f(x)=g(x)*h(x) [that is, two functions multiplied together] To find the derivative, f'(x)=g'(x)*h(x) + g(x)*h'(x) For example, f(x) = (3x 2 )*(cos x ) [g(x)=3x 2 , h(x)=cosx] f'(x) = (6x) ...
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Answered by James W. • Maths tutor
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