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Example Questions
Example Question #1 : Sine
What is the period of 2sin(4Θ)?
None of the answers are correct
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
.
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
.
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 ?
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.
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 #2971 : Act Math
Find the period of the following formula:
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:
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.
The answer is .
Example Question #1 : Sine
What is the domain of the given trigonometric function:
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 : 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.
I only
II only
I and II only
none of the above
II and III only
II only
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 #1 : How To Find The Range Of The Sine
Which of the following represents a sine wave with a range of ?
The range of a sine wave is altered by the coefficient placed in front of the base equation. So, if you have , this means that the highest point on the wave will be at
and the lowest at
. However, if you then begin to shift the equation vertically by adding values, as in,
, then you need to account for said shift. This would make the minimum value to be
and the maximum value to be
. For our question, then, it is fine to use
. The
for the function parameter only alters the period of the equation, making its waves "thinner."
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