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)?
Certainly! Let's break down each of these expressions one by one and determine the values of 'u' that are not permissible.
1.) What values of u are not permissible in the expression csc(u)tan(u)?
To answer this question, we need to understand the trigonometric functions involved. The expression csc(u) represents the cosecant of u, which is equal to 1/sin(u), and tan(u) represents the tangent of u.
In mathematics, there are certain values that are not permissible for these functions. Specifically, the sin(u) function is not defined when its denominator, which is the denominator of csc(u), is equal to zero. Therefore, the values of 'u' that make sin(u) equal to zero are not permissible in the expression csc(u)tan(u).
To find these values, we can set sin(u) equal to zero and solve for u. The solutions to sin(u) = 0 are the values where the denominator is zero, and they occur at integer multiples of pi. So, the values of u that are not permissible in the expression csc(u)tan(u) are given by:
u = n * pi, where n is an integer.
2.) What values of u are not permissible in the expression sin(u)cot(u)?
Similarly, we need to analyze the trigonometric functions involved. The expression sin(u) represents the sine of u, and cot(u) represents the cotangent of u, which is equal to 1/tan(u).
Just like before, we need to find the values of 'u' that make the functions undefined. In this case, cot(u) is not defined when tan(u) is equal to zero. Therefore, the values of 'u' that make tan(u) equal to zero are not permissible in the expression sin(u)cot(u).
We can set tan(u) equal to zero and solve for u. The solutions to tan(u) = 0 are the values where the function is undefined, and they occur at integer multiples of pi. So, the values of u that are not permissible in the expression sin(u)cot(u) are given by:
u = n * pi, where n is an integer.
I hope this explanation clarifies the not permissible values of 'u' in these trigonometric expressions. Let me know if you need any further assistance!