QQuestionMathematics
QuestionMathematics
# What is the equation of the graph below?
y=\cos (x+ 2 \pi)
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Answer
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Step 1:I'll solve this step-by-step, carefully following the LaTeX formatting guidelines:
Step 2:: Identify the Trigonometric Function
- The function is $$y = \cos(x + 2\pi)
The graph shows a cosine function with specific characteristics: - This is the standard cosine function with a horizontal phase shift
Step 3:: Verify Key Characteristics
- Horizontal shift: $$-2\pi$$ units to the left
- Amplitude: 1 (standard cosine function) - Vertical shift: 0 (no vertical translation)
Step 4:: Confirm the Equation
- This is because $$\cos(x + 2\pi) = \cos(x)$$ due to the periodic nature of cosine
- The function looks identical to y = \cos(x)
Final Answer
y = \cos(x + 2\pi)
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