00:01
We have the function, y equals sine x plus sine squared x, and we want to find the equation of the tangent line to that function at the point zero -zero.
00:17
Now, the first thing we should check is that zero -zero is actually a point on the graph of this function.
00:23
If i plug in x equals zero, i get sine of zero, which is zero, plus sine squared of zero, which is zero, which is zero times zero to zero.
00:32
So i get zero and the point zero is indeed on the graph of this function.
00:38
So that's good.
00:39
So we want the equation of a sum tangent line.
00:45
To find the equation of a line in general, it is sufficient to know the slope of the line and a point on the line so that we can then use this standard formula for the equation of a line.
00:59
Y minus y1 equals m times x minus x1 where x1 y1 is a point on our line and m is the slope well we already have a point on our line the tangent line to this function at zero zero passes through zero so we have a point on our line the only thing we need to find is m the slope of our tangent line and the slope of our tangent line at 0 -0 will be the derivative of this function at x equals 0.
01:34
So what we should do next is take the derivative of this function.
01:38
So the derivative of sine x is cosine x.
01:41
And now we use the chain rule.
01:43
We have an inner function, sine of x and an outer function and input raised to the power of 2...