How to find the period of the sine - ACT Math

Card 0 of 6

Question

What is the period of 2sin(4Θ)?

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.

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Question

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

Find the period of

.

Answer

For the function

the period is equal to

in this case

which reduces to .

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Question

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

.

Answer

For the function

the period is equal to

in this case

which reduces to .

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Question

What is the period of the function ?

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

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Question

What is the period of the given trigonometric function:

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

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.

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Question

Find the period of the following formula:

Answer

To find period, simply remember the following formula:

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

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