Question

I'm really confused on these two. Can someone help explain this to me? Thanks! :)


1.) What values of u are not permissible in the expression csc(u)tan(u)?

2.) What values of u are not permissible in the expression sin(u)cot(u)?

Answer 1

both sinx and cosx are defined for every value of x

the problem occurs with the reciprocal functions such as secx or 1/cosx and cscx

also since tanx = sinx/cosx, tanx is undefined if cosx = 0, such as x=90° or π/2
similarly cotx runs into problems when sinx=0 ,such as x=0

when you look at the graphs of the 6 trig functions, you will notice that all of them have vertical asymptotes, that is, they are undefined for certain values, all of them except the sine and cosine function
Find a webpage that shows the 6 graphs, and I am sure you can figure it out

hint: csc(u)tan(u)
= (1/sin(u) )(sin(u)/cos(u))

so all values such that sin(u) = 0 or cos(u) = 0 would not be permissible.
so for 0≤u≤360°
u cannot be 0,90,180,270,360