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 ▸dy/dx = 6x^2 - 3x + 4 when y=14 x=2 Find y in terms of x
How do you solve integrals which are the result of a chain rule e.g. the integral of sin(2x+1)
Given f(x) = (x^(2)+(3*x)+1)/(x^(2)+(5*x)+8), find f'(x) and simplify your answer.
y=x^3-3x^2+2x+5 a)Write down the coordinates of P the point where the curve crosses the x-axis. b)Determine the equation of the tangent to the curve at P. c)Find the coordinates of Q, the point where this tangent meets the curve again.