So let's take a closer look at the sine and cosines graphs, keeping in mind that

**tan**(θ) = sin(θ)/cos(θ). The**tangent**will be**zero**wherever its numerator (the sine) is**zero**. This happens at**0**, π, 2π, 3π, etc, and at –π, –2π, –3π, etc.Accordingly, what is the derivative of tan?

(Math | Calculus | Derivatives | Table Of)

sin x = cos x Proof | csc x = -csc x cot x Proof |
---|---|

cos x = - sin x Proof | sec x = sec x tan x Proof |

tan x = sec^{2} x Proof | cot x = - csc^{2} x Proof |

How do you find the equation of a tangent line?

1)

**Find**the first derivative of f(x). 2) Plug x value of the indicated point into f '(x) to**find**the slope at x. 3) Plug x value into f(x) to**find**the y coordinate of the**tangent**point. 4) Combine the slope from step 2 and point from step 3 using the point-slope formula to**find**the**equation**for the**tangent line**.