Trigonometric Functions and Graphs - Math
Card 0 of 24
Simplify the function below:
Simplify the function below:
We need to use the following formulas:
a) 
and
b) 
We can simplify 
as follows:
We need to use the following formulas:
a)
and
b)
We can simplify
Compare your answer with the correct one above
Which of the following is not in the range of the function 
?
Which of the following is not in the range of the function
The range of the function 
is all numbers between 
and 
(the sine wave never goes above or below this).
Of the choices given, 
is greater than 
and thus not in this range.
The range of the function
Of the choices given,
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What is the period of
?
What is the period of
The period for 
is 
. However, if a number is multiplied by 
, you divide the period 
by what is being multiplied by 
. Here, 
is being multiplied by 
. 
equals 
.
The period for
Compare your answer with the correct one above
Which of the given functions has the greatest amplitude?
Which of the given functions has the greatest amplitude?
The amplitude of a function is the amount by which the graph of the function travels above and below its midline. When graphing a sine function, the value of the amplitude is equivalent to the value of the coefficient of the sine. Similarly, the coefficient associated with the x-value is related to the function's period. The largest coefficient associated with the sine in the provided functions is 2; therefore the correct answer is 
.
The amplitude is dictated by the coefficient of the trigonometric function. In this case, all of the other functions have a coefficient of one or one-half.
The amplitude of a function is the amount by which the graph of the function travels above and below its midline. When graphing a sine function, the value of the amplitude is equivalent to the value of the coefficient of the sine. Similarly, the coefficient associated with the x-value is related to the function's period. The largest coefficient associated with the sine in the provided functions is 2; therefore the correct answer is
The amplitude is dictated by the coefficient of the trigonometric function. In this case, all of the other functions have a coefficient of one or one-half.
Compare your answer with the correct one above
What is the amplitude of 
?
What is the amplitude of
The amplitude of a wave function like 
is always going to be the coefficient of the function. In this case, that is 
.
The amplitude of a wave function like
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What is the local maximum of 
between 
and 
?
What is the local maximum of
The fastest way to solve this problem is to graph it and observe the answer. However, the other option is to think of this equation in terms of period.
When the coefficient of the variable increases, the frequency increases and the period decreases by that rate.
Since our equation is 
, our period will be 
the normal period of a 
wave. Since only the period is changing, the amplitude is not. Therefore the amplitude (the highest and lowest points) of 
will be the same as that of 
. The amplitude of a sine wave is 
, so the amplitude of 
will also be 
.
Therefore, our maximum will be 
.
The fastest way to solve this problem is to graph it and observe the answer. However, the other option is to think of this equation in terms of period.
When the coefficient of the variable increases, the frequency increases and the period decreases by that rate.
Since our equation is
Therefore, our maximum will be
Compare your answer with the correct one above
Simplify the function below:
Simplify the function below:
We need to use the following formulas:
a)
and
b)
We can simplify as follows:
We need to use the following formulas:
a)
and
b)
We can simplify
Compare your answer with the correct one above
Which of the following is not in the range of the function ?
Which of the following is not in the range of the function
The range of the function is all numbers between and (the sine wave never goes above or below this).
Of the choices given, is greater than and thus not in this range.
The range of the function
Of the choices given,
Compare your answer with the correct one above
What is the period of
?
What is the period of
The period for is . However, if a number is multiplied by , you divide the period by what is being multiplied by . Here, is being multiplied by . equals .
The period for
Compare your answer with the correct one above
Which of the given functions has the greatest amplitude?
Which of the given functions has the greatest amplitude?
The amplitude of a function is the amount by which the graph of the function travels above and below its midline. When graphing a sine function, the value of the amplitude is equivalent to the value of the coefficient of the sine. Similarly, the coefficient associated with the x-value is related to the function's period. The largest coefficient associated with the sine in the provided functions is 2; therefore the correct answer is .
The amplitude is dictated by the coefficient of the trigonometric function. In this case, all of the other functions have a coefficient of one or one-half.
The amplitude of a function is the amount by which the graph of the function travels above and below its midline. When graphing a sine function, the value of the amplitude is equivalent to the value of the coefficient of the sine. Similarly, the coefficient associated with the x-value is related to the function's period. The largest coefficient associated with the sine in the provided functions is 2; therefore the correct answer is
The amplitude is dictated by the coefficient of the trigonometric function. In this case, all of the other functions have a coefficient of one or one-half.
Compare your answer with the correct one above
What is the amplitude of ?
What is the amplitude of
The amplitude of a wave function like is always going to be the coefficient of the function. In this case, that is .
The amplitude of a wave function like
Compare your answer with the correct one above
What is the local maximum of between and ?
What is the local maximum of
The fastest way to solve this problem is to graph it and observe the answer. However, the other option is to think of this equation in terms of period.
When the coefficient of the variable increases, the frequency increases and the period decreases by that rate.
Since our equation is , our period will be the normal period of a wave. Since only the period is changing, the amplitude is not. Therefore the amplitude (the highest and lowest points) of will be the same as that of . The amplitude of a sine wave is , so the amplitude of will also be .
Therefore, our maximum will be .
The fastest way to solve this problem is to graph it and observe the answer. However, the other option is to think of this equation in terms of period.
When the coefficient of the variable increases, the frequency increases and the period decreases by that rate.
Since our equation is
Therefore, our maximum will be
Compare your answer with the correct one above
Simplify the function below:
Simplify the function below:
We need to use the following formulas:
a)
and
b)
We can simplify as follows:
We need to use the following formulas:
a)
and
b)
We can simplify
Compare your answer with the correct one above
Which of the following is not in the range of the function ?
Which of the following is not in the range of the function
The range of the function is all numbers between and (the sine wave never goes above or below this).
Of the choices given, is greater than and thus not in this range.
The range of the function
Of the choices given,
Compare your answer with the correct one above
What is the period of
?
What is the period of
The period for is . However, if a number is multiplied by , you divide the period by what is being multiplied by . Here, is being multiplied by . equals .
The period for
Compare your answer with the correct one above
Which of the given functions has the greatest amplitude?
Which of the given functions has the greatest amplitude?
The amplitude of a function is the amount by which the graph of the function travels above and below its midline. When graphing a sine function, the value of the amplitude is equivalent to the value of the coefficient of the sine. Similarly, the coefficient associated with the x-value is related to the function's period. The largest coefficient associated with the sine in the provided functions is 2; therefore the correct answer is .
The amplitude is dictated by the coefficient of the trigonometric function. In this case, all of the other functions have a coefficient of one or one-half.
The amplitude of a function is the amount by which the graph of the function travels above and below its midline. When graphing a sine function, the value of the amplitude is equivalent to the value of the coefficient of the sine. Similarly, the coefficient associated with the x-value is related to the function's period. The largest coefficient associated with the sine in the provided functions is 2; therefore the correct answer is
The amplitude is dictated by the coefficient of the trigonometric function. In this case, all of the other functions have a coefficient of one or one-half.
Compare your answer with the correct one above
What is the amplitude of ?
What is the amplitude of
The amplitude of a wave function like is always going to be the coefficient of the function. In this case, that is .
The amplitude of a wave function like
Compare your answer with the correct one above
What is the local maximum of between and ?
What is the local maximum of
The fastest way to solve this problem is to graph it and observe the answer. However, the other option is to think of this equation in terms of period.
When the coefficient of the variable increases, the frequency increases and the period decreases by that rate.
Since our equation is , our period will be the normal period of a wave. Since only the period is changing, the amplitude is not. Therefore the amplitude (the highest and lowest points) of will be the same as that of . The amplitude of a sine wave is , so the amplitude of will also be .
Therefore, our maximum will be .
The fastest way to solve this problem is to graph it and observe the answer. However, the other option is to think of this equation in terms of period.
When the coefficient of the variable increases, the frequency increases and the period decreases by that rate.
Since our equation is
Therefore, our maximum will be
Compare your answer with the correct one above
Simplify the function below:
Simplify the function below:
We need to use the following formulas:
a)
and
b)
We can simplify as follows:
We need to use the following formulas:
a)
and
b)
We can simplify
Compare your answer with the correct one above
Which of the following is not in the range of the function ?
Which of the following is not in the range of the function
The range of the function is all numbers between and (the sine wave never goes above or below this).
Of the choices given, is greater than and thus not in this range.
The range of the function
Of the choices given,
Compare your answer with the correct one above