# What is the equation of the tangent line of #f(x)=sin x + sin^2 x# at #x=0#?

##### 1 Answer

#### Explanation:

This problem can be tackled in 3 steps:

**1. Figure out the gradient of the line using the derivative of the function and the given #x# value.
2. Use the given #x# value and #f(x)# to find #C#.
3. Put values into the standard equation of a straight line.**

The equation of a line

**1.** We'll begin by working out

Where the chain rule has been used on the

Since we want to find the tangent at

Thus

Step 1 is complete.

**2.** We must now find

Use

Thus

So, using

Thus we have our value for

**3.** We can now write:

Indeed we see that if we plot both on the same graph we get a line intersection at a tangent exactly where we would expect: