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)?

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

I'd be happy to help you with these two questions!

1.) In the expression csc(u)tan(u), the values of u that are not permissible are the ones that would result in division by zero. Let's break it down step by step:

First, let's consider the csc(u) part. The csc function represents the cosecant function, which is equal to 1/sin(u). The sine function, sin(u), has values of zero at u = 0, π, 2π, and so on. So, for csc(u) to be defined, sin(u) cannot be equal to zero. Therefore, the values of u that are not permissible in csc(u) are u = 0, π, 2π, and so on.

Next, let's look at the tan(u) part. The tangent function, tan(u), has values of infinity or negative infinity at u = π/2, 3π/2, 5π/2, and so on. This means that for tan(u) to be defined, u cannot be equal to π/2, 3π/2, 5π/2, and so on.

To determine the values of u that are not permissible in the expression csc(u)tan(u), we need to find the values that satisfy both conditions. Therefore, the values of u that are not permissible in this expression are u = 0, π, 2π, π/2, 3π/2, 5π/2, and so on.

2.) Similarly, for the expression sin(u)cot(u), the values of u that are not permissible are the ones that would result in division by zero. Let's break it down step by step:

The sine function, sin(u), has values of zero at u = 0, π, 2π, and so on. Therefore, sin(u) cannot be equal to zero for the expression to be defined. This means that u = 0, π, 2π, and so on are not permissible values.

Next, the cot(u) part represents the cotangent function, which is equal to 1/tan(u). The tangent function, tan(u), has values of infinity or negative infinity at u = π/2, 3π/2, 5π/2, and so on. So, for cot(u) to be defined, u cannot be equal to π/2, 3π/2, 5π/2, and so on.

To find the values of u that are not permissible in the expression sin(u)cot(u), we need to find the values that satisfy both conditions. Therefore, the values of u that are not permissible are u = 0, π, 2π, π/2, 3π/2, 5π/2, and so on.

I hope that helps clarify these two expressions for you! Let me know if you have any more questions.