# What is the instantaneous velocity of an object moving in accordance to # f(t)= (sin2tcost,tant-sect ) # at # t=(13pi)/12 #?

##### 2 Answers

#### Explanation:

Let's derive the vectorial function

we get

that is

and its length is

The instantaneous velocity

#### Explanation:

Differentiate the equation,

Use the product rule to differentiate the equation,

Solve the chain rule,

Substitute in the derivatives that we calculated:

The speed will be the above evaluated at

The angle with respect to horizontal is the inverse tangent of the speed: