How Can I Correctly Graph the Trigonometric Function f(x) = 2cos(3x+pi/2) -1?

[dash00]

i have a problem graphing trig functions such as f(x) = 2cos(3x+pi/2) -1

i know this should be very simple but i am missing something

can someone explain the way youd go about graphing this
amp= 2
period = 2pi/3
y trans = -1
x trans = (pi/2)/3 [right?]

so when i try graph it my answer is wrong, what am i missing? is it something to do with the smaller period, need help , please!

 

[dextercioby]

HINT:$$\cos \left(3x+\frac{\pi}{2}\right)=-\sin 3x$$

Daniel.

 

[tacman]

Graphing trigonometric functions can be tricky, but with some practice and understanding of the key components, it can become easier. Let's break down the given function f(x) = 2cos(3x+pi/2) -1 and discuss the steps to graph it correctly.

Step 1: Identify the amplitude and period

The amplitude of a trigonometric function is the distance from the midline to the highest or lowest point on the graph. In this case, the amplitude is 2. The period of a trigonometric function is the length of one complete cycle. To find the period, we use the formula P = 2pi/b, where b is the coefficient of x. In this case, b = 3, so the period is 2pi/3.

Step 2: Determine the phase shift

The phase shift is the horizontal translation of the function. It tells us how much the graph has shifted to the left or right. To find the phase shift, we use the formula c/b, where c is the constant term in the function. In this case, c = pi/2, and b = 3, so the phase shift is (pi/2)/3 or pi/6. This means that the graph has shifted pi/6 units to the left.

Step 3: Find the vertical translation

The vertical translation, also known as the y-intercept, tells us how much the graph has shifted up or down. In this case, the function is -1, which means the graph has shifted down 1 unit.

Step 4: Plot key points

To graph the function, we need to plot some key points. We can find these points by plugging in different values for x and solving for y. Here are some key points to plot:

x = 0, y = 1
x = pi/6, y = 1
x = pi/3, y = -1
x = pi/2, y = -3
x = 2pi/3, y = -1
x = 5pi/6, y = 1
x = pi, y = 3

Step 5: Plot the points and connect them with a smooth curve

Using the key points we found, we can now plot them on a graph and connect them with a smooth curve. Remember to label the axes and include the amplitude, period, and