## anonymous one year ago What are the domain of these two functions:

1. anonymous

$y=-3\sec(\pi-2x)+5$

2. anonymous

$y=-2\sin(5/4x)$

3. anonymous

@Nnesha

4. anonymous

5. anonymous

@Vocaloid

6. anonymous

Domain represents the value for x thus in the second equation is there any value that x cannot be?

7. anonymous

the sine curve has its domain unrestricted where as the secant function has vertical asymptotes, hence a restricted domain.

8. anonymous

therefore the domain for the first function is (-infinity,infinity)

9. anonymous

but I do not know the domain for the second function, what is it? @Deeezzzz

10. anonymous

Are you familiar with finding the period of the secant func?

11. anonymous

yes

12. anonymous

The period of the second function is 2

13. anonymous

@Deeezzzz

14. 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.

15. mathstudent55

In the second function, you have the sine function. The sine function is defined for every value of theta.

16. anonymous

wait, so for the second function the domain is (-infinity,infinity)

17. mathstudent55

yes

18. anonymous

I still dont get the domain for the first function

19. mathstudent55

There is no restriction on the domain of the sine function.

20. anonymous

how would i write it down in terms of interval notation

21. mathstudent55

Where is the cosine equal to zero?

22. anonymous

its undefined?

23. anonymous

@mathstudent55

24. mathstudent55

The figure below shows where the cosine equals zero. It is at those points where the secant is undefined. |dw:1438040478384:dw|

25. mathstudent55

The first function has a secant, so its domain is all reals except for integer multiples of $$\dfrac{\pi}{2}$$.