Math Problem Statement

gambarlah grafik fungsi y = 2 sin x-3 dan y = 2 cos x - 3 untuk 0 derajat kurang dari samadengan x kurang dari samadengan 360 derajat pada satu bidang koordinat

Solution

Here is the graph showing the two functions:

  • y = 2sin(x) - 3 in red
  • y = 2cos(x) - 3 in blue

Both functions are plotted on the interval from 0° to 360°.

Would you like further details on how to interpret or analyze these graphs? Let me know if you have any other questions!

Here are five related questions you could explore:

  1. How do phase shifts affect the graphs of sine and cosine functions?
  2. What is the impact of changing the amplitude in sinusoidal functions?
  3. How can we find the period of the functions y = 2sin(x) - 3 and y = 2cos(x) - 3?
  4. What happens if the vertical shift is changed to a different value, like -2 or -4?
  5. How can we determine the maximum and minimum values for these functions?

Tip: To analyze sinusoidal functions, always look at their amplitude (stretching factor), period (frequency), phase shift (horizontal shift), and vertical shift, as they define the shape and position of the graph.

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Math Problem Analysis

Mathematical Concepts

Trigonometric Functions
Graphing
Sine and Cosine Functions

Formulas

y = 2sin(x) - 3
y = 2cos(x) - 3

Theorems

Graphing of Sinusoidal Functions
Amplitude, Period, Phase Shift, and Vertical Shift

Suitable Grade Level

Grades 10-12