### All ACT Math Resources

## Example Questions

### Example Question #1 : Sine

What is the period of 2sin(4Θ)?

**Possible Answers:**

None of the answers are correct

**Correct answer:**

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 #1 : How To Find The Period Of The 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

.

**Possible Answers:**

**Correct answer:**

For the function

the period is equal to

in this case

which reduces to .

### Example Question #2 : How To Find The Period Of The 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

.

**Possible Answers:**

**Correct answer:**

For the function

the period is equal to

in this case

which reduces to .

### Example Question #3 : How To Find The Period Of The Sine

What is the period of the function ?

**Possible Answers:**

**Correct answer:**

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 #4 : How To Find The Period Of The Sine

What is the period of the given trigonometric function:

. Leave your answer in terms of , simplify all fractions.

**Possible Answers:**

**Correct answer:**

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 #5 : How To Find The Period Of The Sine

Find the period of the following formula:

**Possible Answers:**

**Correct answer:**

To find period, simply remember the following formula:

where B is the coefficient in front of x. Thus,