how do you find the domain of

y=sqrt(tanx)
and
y=x/cosx


I can't figure these out for the life of me! Yikesss

The domain is the set of values that the independent variable can take on for the function be valid. Here that means finding the set of values of x that would be allowable. Here's a hint for the first one - you can't take the square root of a negative number, so therefore tan(x) must be greater than or equal to zero. Now, what set of values of x lead to tan(x) meeting that condition? Can you take it from here?

A square root function must have a non-negative domain. Furthermore, there are certain points for which tan is undefined. Combine the two and you've got your first question answered. For your second question, denominators must be non-zero. Any value that would cause your denominator to be 0 must be excluded from the domain. As these are trigonometric functions and are therefore periodic is there a specified interval stated for these problems?