Hi, I Know what to do, find the first derivative. But i get stuck on a line which can't find the exact value.
Question: Find the gradient of the tangent to the curve y = 3cos2x at the point where x = pi/6.
dy/dx = -6sin2x
y'(pi/6) = -6sin(2*pi/6)
how do I simplify that? I'm totally lost as of what to do next.
PS: On another note what does d/dx mean as compared to dy/dx?
Because . If you couldn't see that, no wonder you have problems with this!
Also radians is the same as degrees. And 60 degrees is the measure of each of the angles in an equilateral triangle. Imagine an equilateral triangle with each side of length 1. Drop a perpendicular from one vertex to the opposite side. That will also bisect the opposite side so you now have two right triangles with one leg of length 1/2 and hypotenuse of length 1. By the Pythagorean theorem, where b is the length of the other leg- the perpendicular. Then so . Sine is "opposite side over hypotenuse so .