How can you use a table of values to graph y=cosx-2?

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SUMMARY

The discussion focuses on graphing the function y=cos(x)-2 using a table of values. The user successfully identified that the transformation involves shifting the graph of y=cos(x) down by 2 units, resulting in a new y-intercept at -1. The transformation follows the standard form y=acos(k(x-d))+c, where -2 represents the vertical shift (c value). The conversation clarifies that the input for trigonometric functions can be in degrees or radians, countering a common misconception.

PREREQUISITES
  • Understanding of trigonometric functions, specifically cosine.
  • Familiarity with graph transformations, including vertical shifts.
  • Knowledge of the standard form of trigonometric equations: y=asin(k(x-d))+c and y=acos(k(x-d))+c.
  • Ability to create and interpret tables of values for functions.
NEXT STEPS
  • Study the properties of the cosine function and its graph.
  • Learn about graph transformations, focusing on vertical and horizontal shifts.
  • Explore the differences between degrees and radians in trigonometric functions.
  • Practice graphing other trigonometric functions using tables of values.
USEFUL FOR

Students, educators, and anyone interested in mastering graphing techniques for trigonometric functions, particularly those focusing on transformations and the cosine function.

supernova1203
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Graph the function y=cosx-2I have already graphed this, there are several methods to solve this, i opted to use table of values to find all the coordinates to y=cosx, then moved all the y coordinates of each point 2 units down, and the y int was at -1...would this method result in the correct graph?

the -2 is the c value I am assuming because the d value is ALWAYS in degrees, atleast in these instances.

y=asin(k(x-d))+c

y=acos(k(x-d))+c

what y int do you guys get? Does what i have done make sense?

this is to transform the function from base to y=cosx-2
 
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"I have already graphed this, there are several methods to solve this, i opted to use table of values to find all the coordinates to y=cosx, then moved all the y coordinates of each point 2 units down, and the y int was at -1...


would this method result in the correct graph? ...Does what i have done make sense?"


Yes. I don't know how you would get it really, or anything else, if it doesn't make sense.

Now I hope you will be confident to do the other ones and make sense.
 
supernova1203 said:
Graph the function y=cosx-2


I have already graphed this, there are several methods to solve this, i opted to use table of values to find all the coordinates to y=cosx, then moved all the y coordinates of each point 2 units down, and the y int was at -1...


would this method result in the correct graph?
Yes. If you know what the graph of y = f(x) looks like, the graph of y = f(x) - 2 will be the first graph translated (shifted) down by two units.
supernova1203 said:
the -2 is the c value I am assuming because the d value is ALWAYS in degrees, atleast in these instances.
That's not generally true. The input values to the trig functions can be in degrees or radians, and rarely, grads, another kind of angle measure in which 100 grads make up a right angle.
supernova1203 said:
y=asin(k(x-d))+c

y=acos(k(x-d))+c

what y int do you guys get? Does what i have done make sense?

this is to transform the function from base to y=cosx-2
 

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