## Circular Functions

Examples of Circular functions are sin(x), cos(x) and tan(x), they are also known as trigonometric functions.

### Differentiation of Sin

The derivative of sin is supplied in the formula sheet as:

When we find the derivative of a sin function we find the derivative of what is inside the brackets and multiply by cos of what was inside the sin brackets.

#### Example of Sin Differentiation

**Step 1** is to find the derivative of what is inside the brackets.

**Step 2 ** is to convert the sin function to a cos function while keeping what is in the brackets the same.

**Step 3 **is to multiply the first two steps together.

### Differentiation of Cos

The derivative of sin is supplied in the formula sheet as:

When we find the derivative of a cos function we find the derivative of what is inside the brackets and multiply by the negative sin of what was inside the cos brackets.

#### Example of Cos Differentiation

**Step 1** is to find the derivative of what is inside the brackets.

**Step 2 ** is to convert the sin function to a cos function while keeping what is in the brackets the same.

**Step 3 **is to multiply the first two steps together.

### Differentiation of Tan

The derivative of sin is supplied in the formula sheet as:

When we find the derivative of a sin function we find the derivative of what is inside the brackets and multiply by cos of what was inside the sin brackets.

#### Example of Tan Differentiation

**Step 1** is to again find the derivative of what is inside the brackets.

**Step 2 ** is to convert the tan function to a one over cos squared or a sec squared function while keeping what is in the brackets the same. In this instance we will just keep it in terms of cos, although either is correct.

**Step 3 **is to multiply the first two steps together.

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