## Example Questions

### Example Question #1 : Sine

What is the period of 2sin(4Θ)?   None of the answers are correct  Explanation:

The period of sinΘ is 2Π, so we set the new angle equal to the base period of 2Π and solve for Θ.

So 4Θ = 2Π and Θ = Π/2.

### Example Question #2 : Sine

A function with period P will repeat on intervals of length P, and these intervals are referred to as periods.

Find the period of .     Explanation:

For the function the period is equal to in this case which reduces to .

### Example Question #1 : Sine

A function with period P will repeat on intervals of length P, and these intervals are referred to as periods.

Find the period of the function .     Explanation:

For the function the period is equal to in this case which reduces to .

### Example Question #1 : Sine

What is the period of the function ?      Explanation:

To find the period of Sine and Cosine functions you use the formula: where comes from . Looking at our formula you see b is 4 so ### Example Question #5 : Sine

What is the period of the given trigonometric function: . Leave your answer in terms of , simplify all fractions.      Explanation:

To find the period of a sine, cosine, cosecant, or secant funciton use the formula: where comes from the general formula: . We see that for our equation and so the period is when you reduce the fraction.

### Example Question #6 : Sine

Find the period of the following formula:       Explanation:

To find period, simply remember the following formula: where B is the coefficient in front of x. Thus, ### All ACT Math Resources 