Trigonometric Functions Graphing

In summary, the person is trying to graph a trigonometric function and has run into a problem. They have added a new rule to help them with the problem.
  • #1
majinknight
53
0
Ok I have hit a little bumb in the road on my trigonometric function learning. Ok i need to graph the function y=3cos2(x-120degrees)-3, for x is less than or equal to 360degrees but is greater than or equal to -360degrees. Ok so i know the:
verticle translation is 3 down
the phase shift is 120 to the right
amplitude is 3
period is 180 degrees
and so i have the horizontal scale at 15degrees.
so far so good?

Ok now here is the one problem, i do not know if i am to go and as sin grpahs go it starts at highest then to middle then lowest then middle then highest and is finished one wave. Well since my hs=15 each line on graph is 15. now i start on 120 as i have to and herei s my question. When i go down to the middle line which would be -3 would it be on the interval of 150degrees or 135 degrees? Or am i doing it wrong as i thought period meant one full wavelength is 180 degrees so it is making me think i am doing it wrong. Please help if possible.
 
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  • #2
Alright from this equation y=3cos(2(x-120degrees))-3

I have the rule (.5x+120, 3y-3) is that what you have?
then with a cosine funtion you start on the y-axis at point (0,1) and then you move to (90, 0) then to (180, -1) then to (270, 0) then to (360, 1) correct? so what you are correct with your beginning point being (120, 0) {thats what you have right} what i normally do when approaching this type of problem is very very basic.. because i am a square who doesn't like to very risky.. i used my rule with an x/y chart. soo...

original points
x | y
0 | 1
90 | 0
180 | -1
270 | 0
360 | 1

New rule added ones
x | y
120 | 0
165 | -3
210 | -6
255 | -3

so you are basically adding 45 to the x every time and using 0, -3, and -6 over and over again.. does this answer your question and help you at all. I am slightly rusty on all the information on this because i havnt worked with this in about 3months.
 
  • #3
Ok well i figured out what i did wrong so the help isn't needed but thank you anyways
 

What are trigonometric functions?

Trigonometric functions are mathematical functions that relate the angles of a triangle to the lengths of its sides. They are commonly used in geometry and calculus to solve problems involving triangles and circular motion.

What are the basic trigonometric functions?

The basic trigonometric functions are sine, cosine, and tangent. These functions are used to calculate the ratio of the sides of a right triangle.

How do you graph trigonometric functions?

To graph trigonometric functions, you first need to identify the amplitude, period, and phase shift of the function. Then, you can use these values to plot points on the graph and connect them to create a curve.

What is the unit circle and how is it related to trigonometric functions?

The unit circle is a circle with a radius of 1 that is centered at the origin of a coordinate plane. It is used to represent the values of trigonometric functions at different angles. The x-coordinate of a point on the unit circle represents the cosine function, while the y-coordinate represents the sine function.

What are the common applications of trigonometric functions?

Trigonometric functions have many practical applications, such as in navigation, engineering, and physics. They are used to calculate distances and angles in real-world scenarios, and in fields such as architecture and astronomy.

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