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f(x) = sinx. Using differentiation from first principles find the exact value of f' (π/6).

The derivative of the function where x=π/6 is defined asThe limit as h->0 of [sin(h+π/6)-sin(π/6)]/hUsing the double angle formula, sin(h+π/6) = sin(h)cos(π/6) + cos(h)sin(π/6) = √3sin(h)/2 + cos(h)si...

Answered by Maths tutor
6136 Views

There is a spinner game at a fair. The spinner is numbered with all even numbers from 2 to 12. Each section is equal in size. Dan has numbers 4 and 10. What is the probability that he wins a prize? Give your answer as a fraction in its simplest form.

The even numbers from 2 to 12: 2, 4, 6, 8, 10, 12That means there are 6 numbers on the spinner If Dan has 4 and 10 and all the portions are the same, the chances of landing on 4 or 10 is 2/6Simplifying th...

Answered by Katherine B. Maths tutor
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If I know the length of the hypotenuse and one angle, how do i find the length of the side opposite to the angle?

In this problem, we are concerned with the hypotenuse and the opposite sides of the right angle triangles. From SOHCAHTOA we can see that the opposite (O) and hypotenuse (H) are associated with the sine f...

Answered by Jake C. Maths tutor
2472 Views

What is the equation of the straight line passing through the points (2,3) and (3,5)?

There are three steps to solving these types of straight line problems. 1) Find the gradient (slope) of the line. 2) Find the point slope formula. 3) Solve for y.1) The gradient (m) of the line bet...

Answered by Omar M. Maths tutor
4580 Views

What are the stationary points of the curve (1/3)x^3 - 2x^2 + 3x + 2 and what is the nature of each stationary point.

Firstly, a stationary point is a point on the curve where the gradient of the tangent line is equal to 0. Here, this occurs at points where the first derivative of f(x) = 1/3x

Answered by Omar M. Maths tutor
6397 Views

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