anonymous
  • anonymous
What are the domain of these two functions:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[y=-3\sec(\pi-2x)+5\]
anonymous
  • anonymous
\[y=-2\sin(5/4x)\]
anonymous
  • anonymous
@Nnesha

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anonymous
  • anonymous
somebody please help
anonymous
  • anonymous
@Vocaloid
anonymous
  • anonymous
Domain represents the value for x thus in the second equation is there any value that x cannot be?
anonymous
  • anonymous
the sine curve has its domain unrestricted where as the secant function has vertical asymptotes, hence a restricted domain.
anonymous
  • anonymous
therefore the domain for the first function is (-infinity,infinity)
anonymous
  • anonymous
but I do not know the domain for the second function, what is it? @Deeezzzz
anonymous
  • anonymous
Are you familiar with finding the period of the secant func?
anonymous
  • anonymous
yes
anonymous
  • anonymous
The period of the second function is 2
anonymous
  • anonymous
@Deeezzzz
mathstudent55
  • mathstudent55
The first function uses the secant function. Remember this identity. \(\sec \theta = \dfrac{1}{\cos \theta}\) The secant is not defined where the cosine equals zero.
mathstudent55
  • mathstudent55
In the second function, you have the sine function. The sine function is defined for every value of theta.
anonymous
  • anonymous
wait, so for the second function the domain is (-infinity,infinity)
mathstudent55
  • mathstudent55
yes
anonymous
  • anonymous
I still dont get the domain for the first function
mathstudent55
  • mathstudent55
There is no restriction on the domain of the sine function.
anonymous
  • anonymous
how would i write it down in terms of interval notation
mathstudent55
  • mathstudent55
Where is the cosine equal to zero?
anonymous
  • anonymous
its undefined?
anonymous
  • anonymous
@mathstudent55
mathstudent55
  • mathstudent55
The figure below shows where the cosine equals zero. It is at those points where the secant is undefined. |dw:1438040478384:dw|
mathstudent55
  • mathstudent55
The first function has a secant, so its domain is all reals except for integer multiples of \(\dfrac{\pi}{2} \).

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