Finding the x and y intercepts

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SUMMARY

The discussion focuses on finding the x and y intercepts of the function f(x) = sin(x)/(1 + cos(x)). The correct y-intercept is determined by setting x = 0, yielding the point (0, 0). The x-intercept is found by evaluating f(0), resulting in the point (0, 0). However, the original poster incorrectly identified the y-intercept as (0, π) and confused the definitions of x and y intercepts, leading to a violation of the function's definition by suggesting two points with the same x-value.

PREREQUISITES
  • Understanding of trigonometric functions and their properties
  • Knowledge of intercepts in Cartesian coordinates
  • Familiarity with the definition of a function
  • Basic algebraic manipulation skills
NEXT STEPS
  • Review the properties of trigonometric functions, specifically sin(x) and cos(x)
  • Study the concept of intercepts in graphing functions
  • Learn about the implications of the definition of a function
  • Practice solving equations involving trigonometric identities
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Students studying calculus, mathematics educators, and anyone looking to clarify their understanding of intercepts in trigonometric functions.

vane92
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f(x)=sin(x)/(1+cos(x))
So I set it equal to zero to find the y-intercept
sin(x)=0(1+cos(x))
x= 0,∏ so the y-int: (0,0) and (0,∏)

To find the x intercept I would substitute 0 for x so,
sin(0)/(1+cos(0))=y
0/1+1=y
y=0 so the x-int: (0,0)

would that be right?
 
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Unfortunately, there are a few mistakes. Firstly, you are confusing the x and y-axis a bit. To find the y-intercept you would set x=0 (the y-axis has equation x=0) and vice versa. Secondly, you listed the points (0,0) and (0,π). You can not have two points on a function with the same x-value. It violates the definition of a function. Surely you meant the points (0,0) and (π,0). Finally, you incorrectly solved the equation [tex]{\frac{\sin x }{1+cos x}}=0[/tex]

Not only is it necessary for [itex]sin x[/itex] to be zero, but [itex]1+ cos x[/itex] must also be nonzero. [itex]x = \pi[/itex] does not fulfill this second requirement.

Edit: This post should probably be in the Homework & Coursework Questions section.
 

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