QQuestionMathematics
QuestionMathematics
What is the difference between the cosine and sine graphs?
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Step 1:I'll explain the differences between the cosine and sine graphs step by step:
Step 2:: Basic Function Definitions
- $$\cos( heta)$$ starts at the origin (0,0) with a slope of 0
The sine and cosine functions are both trigonometric functions, but they have distinct characteristics:
Step 3:: Phase Shift
- This means $$\sin( heta) = \cos( heta - \frac{ pi}{2})
The key difference is their phase relationship:
Step 4:: Graphical Representation
* Crosses x-axis at $$\frac{ pi}{2}
* Passes through (0,0) * Rises from the origin with a positive slope * Starts at (0,1) * Begins with a horizontal tangent * Reaches maximum of 1 at 0
Step 5:: Symmetry
- $$\sin( heta)$$ is an odd function (symmetric about the origin)
- \cos( heta) is an even function (symmetric about the y-axis)
Final Answer
While both are periodic functions with amplitude 1, the cosine graph starts at (0,1) and is shifted \frac{ pi}{2} to the left compared to the sine graph.
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