00:01
Okay, in order to find the tangent and the normal line of this graph, 6 cosine of x, at this specific point, we will be needing the point slope formula.
00:14
Now, in order to get the equation of a line, we need both a point and the slope of that line.
00:22
So we will need to take our derivative.
00:26
So here, our derivative, y prime, is equal to the derivative, of cosine of x is negative sine of x, so our derivative will be negative 6, sine of x.
00:40
Now, we will find what the derivative is at x equals pi over 3, which will give us negative 6 times the sign of pi over 3.
00:58
Now the sign of pi over 3 is radical 3 over 2, and this will give us a slope of negative 3, radical 3 at that specific point.
01:19
So the equation for our tangent line will be y minus 3 is equal to negative 3, radical 3 times x minus, pi over 3...