Finding points on sine graph with same gradient

[TheBelgiumGuy]

Hi eveyone, i hope you can help me! Please excuse my English.

My problem is this.... It is written f(x)=sin(2x)+(1/2). It says 'When x=(3/5), y=1.43. m at the position is 0.725. Find the next point on the function that has the exact same value for m and prove this using algebra.'

I have graphed this function and I know m is the gradient and I have differentiated f(x) to f'(x) & f'(x) is 2cos(2x).

How is the rest of the procedure to find the next pair of coordinates on f(x)=sin(2x)+(1/2) that has a gradient of 0.725?

Thx all - from Belgium!

 

[HallsofIvy]

You say you know the gradient, at any x, is \(\displaystyle 2 cos(2x)\). Saying that the gradient is 0.725 means that \(\displaystyle 2 cos(2x)= 0.725\). Solve that equation for x. Then find the corresponding y.