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

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SUMMARY

The discussion centers on graphing the trigonometric function f(x) = 2cos(3x + π/2) - 1. Key parameters identified include an amplitude of 2, a period of 2π/3, a vertical translation of -1, and a horizontal translation calculated as (π/2)/3. The user, Daniel, struggles with the graphing process, particularly in relation to the function's period and transformation, and is reminded that cos(3x + π/2) can be rewritten as -sin(3x) to aid in graphing.

PREREQUISITES
  • Understanding of trigonometric functions and their properties
  • Knowledge of amplitude, period, and phase shifts in graphing
  • Familiarity with transformations of trigonometric functions
  • Ability to manipulate trigonometric identities, specifically cos and sin
NEXT STEPS
  • Study the properties of trigonometric functions, focusing on amplitude and period
  • Learn how to apply horizontal and vertical translations to graphing
  • Explore the relationship between cosine and sine functions, particularly transformations
  • Practice graphing various trigonometric functions with different parameters
USEFUL FOR

Students and educators in mathematics, particularly those focusing on trigonometry, as well as anyone seeking to improve their skills in graphing trigonometric functions.

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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 :frown:

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!
 
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HINT:[tex]\cos \left(3x+\frac{\pi}{2}\right)=-\sin 3x[/tex]

Daniel.
 

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