All Trigonometry Resources
Example Question #1 : Graphing Sine And Cosine
The function shown below has an amplitude of ___________ and a period of _________.
The amplitude is always a positive number and is given by the number in front of the trigonometric function. In this case, the amplitude is 4. The period is given by , where b is the number in front of x. In this case, the period is .
Example Question #2 : Graphing Sine And Cosine
This is the graph of what function?
The amplitude of the sine function is increased by 3, so this is the coefficient for . The +2 shows that the origin of the function is now at instead of
Example Question #3 : Graphing Sine And Cosine
Which of the following graphs does not have a -intercept at ?
The y-intercept is the value of y when .
Recall that cosine is the value of the unit circle. Thus, , so it works.
Secant is the reciprocal of cosine, so it also works.
Also recall that . Thus, the only answer which is not equivalent is .
Example Question #4 : Graphing Sine And Cosine
What is an equation for the above function?
The amplitude of a sinusoidal function is unless amplified by a constant in front of the equation. In this case, the amplitude is , so the front constant is .
The graph moves through the origin, so it is either a sine or a shifted cosine graph.
It repeats once in every , as opposed to the usual , so the period is doubled, the constant next to the variable is .
The only answer in which both the correct amplitude and period is found is:
Example Question #5 : Graphing Sine And Cosine
Let be a function defined as follows:
The 3 in the function above affects what attribute of the graph of ?
The period of the function is indicated by the coefficient in front of ; here the period is unchanged.
The amplitude of the function is given by the coefficient in front of the ; here the amplitude is 2.
The phase shift is given by the value being added or subtracted inside the function; here the shift is units to the right.
The only unexamined attribute of the graph is the vertical shift, so 3 is the vertical shift of the graph.
Example Question #6 : Graphing Sine And Cosine
Which graph correctly illustrates the given equation?
The simplest way to solve a problem like this is to determine where a particular point on the graph would lie and then compare that to our answer choices. We should first find the y-value when the x-value is equal to zero. We will start by substituting zero in for the x-variable in our equation.
Now that we have calculated the y-value we know that the correct graph must have the following point:
Unfortunately, two of our graph choices include this point; thus, we need to pick a second point.
Let's find the y-value when the x-variable equals the following:
We will begin by substituting this into our original equation.
Now we need to investigate the two remaining choices for the following point:
Unfortunately, both of our remaining graphs have this point as well; therefore, we need to pick another x-value. Suppose the x-variable equals the following:
Now, we must substitute this value into our given equation.
Now, we can look for the graph with the following point:
We have narrowed in on our final answer; thus, the following graph is correct: