# ACT Math : Sine

## Example Questions

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### 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 #2962 : Act Math

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 #4 : 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:

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 #51 : Trigonometry

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,

### Example Question #7 : Sine

Find the domain of the function:

Explanation:

The function  is related to the parent function , which has a domain of .

The value of theta for  has no restriction and is valid for all real numbers.

### Example Question #2971 : Act Math

What is the domain of the given trigonometric function:

Explanation:

For both Sine and Cosine, since there are no asymptotes like Tangent and Cotangent functions, the function can take in any value for . Thus the domain is:

### Example Question #1 : How To Find The Range Of The Sine

Which of the following statements is (are) true:

I. The domain of the tangent function is all real numbers

II. The range of the sine function is all real numbers

III. The periods of the tangent, sine, and cosine functions are the same.

II only

I only

I and II only

none of the above

II and III only

II only

Explanation:

The domain of the tangent function does not include any values of x that are odd multiples of π/2 .

The range of the sine function is from [-1, 1].

The period of the tangent function is π, whereas the period for both sine and cosine is 2π.

### Example Question #10 : Sine

Which of the following represents a sine wave with a range of ?