How to find the period of the tangent - ACT Math
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Which of the following equations represents a tangent function with a period that is 
radians?
Which of the following equations represents a tangent function with a period that is
The standard period of a tangent function is 
radians. In other words, it completes its entire cycle of values in that many radians. To alter the period of the function, you need to alter the value of the parameter of the trigonometric function. You multiply the parameter by the number of periods that would complete in 
radians. With a period of 
, you are quadrupling your method. Therefore, you will have a function of the form:
Since 
and 
do not alter the period, these can be anything.
Therefore, among your options, 
is correct.
The standard period of a tangent function is
Since
Therefore, among your options,
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Which of the following represents a tangent function that has a period half that of one with a period of 
?
Which of the following represents a tangent function that has a period half that of one with a period of
The standard period of a tangent function is 
radians. In other words, it completes its entire cycle of values in that many radians. To alter the period of the function, you need to alter the value of the parameter of the trigonometric function. You multiply the parameter by the number of periods that would complete in 
radians. With a period of 
, you are multiplying your parameter by 
. Now, half of this would be a period of 
. Thus, you will have a function of the form:
Since 
and 
do not alter the period, these can be anything.
Therefore, among your options, 
is correct.
The standard period of a tangent function is
Since
Therefore, among your options,
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What is the period of the following tangent function?
What is the period of the following tangent function?
The period of the tangent function defined in its standard form 
has a period of 
. When you multiply the argument of the trigonometric function by a constant, you shorten its period of repetition. (Think of it like this: You pass through more iterations for each value 
that you use.) If you have 
, this has one fifth of the period of the standard tangent function. In the equation given, none of the other details matter regarding the period. They alter other aspects of the equation (its "width," its location, etc.). The period is altered only by the parameter. Thus, the period of this function is 
of 
, or 
.
The period of the tangent function defined in its standard form
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What is the period of the following trigonometric equation:
What is the period of the following trigonometric equation:
For tangent and cotangent the period is given by the formula:
where 
comes from 
.
Thus we see from our equation 
and so
.
For tangent and cotangent the period is given by the formula:
Thus we see from our equation
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What is the period of the trigonometric function given by:
?
What is the period of the trigonometric function given by:
To find the period of a tangent funciton use the following formula:
where 
comes from 
.
thus we get that 
so 
To find the period of a tangent funciton use the following formula:
thus we get that
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What is the period of the following trigonometric function:
What is the period of the following trigonometric function:
To find the period of a tangent or cotangent function use the following formula:
from the general tirogonometric formula:
Since we have,
we have
.
Thus we get that
To find the period of a tangent or cotangent function use the following formula:
from the general tirogonometric formula:
Since we have,
we have
Thus we get that
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