Work out the angle between the two tangents of the curve y = sin(x) at y = 0 and y = 1
First we take the derivative of the function, this gives us dy/dx = cos(x)
Now we work out the different x values for y = 0 and y = 1.
sin(x) = 0 => x = 0, sin(x) = 1 => x = pi/2 (90 degrees)
We then substitute these values into dy/dx which gives us two gradients of 1 and 0 respectively
We can then work out the angle between these two values as the difference between the tangents of the two gradients
(angle = tan(m), this gives us the answer of 45 degrees (angle = tan(1) - tan(0))
KJ
Related Maths Scottish Highers answers
All answers ▸How do you solve integrals which are the result of a chain rule e.g. the integral of sin(2x+1)
Calculate the rate of change of y(t) = 1/(4t), when t = 8
Given x^3 + 4x^2 + x - 6 = 0 , and one of the factors of this equation is (x-1), factorise and hence compute the other solutions for the eqaution.
Calculate the rate of change of d(t )=2/(3t), t ≠ 0, when t=6.