using csc = 3.75, solve for sides:

Question

a= 3
b= ?
c= ?

and the remaining five trigonometric functions:
sin= (1/3.75)
cos= ?
tan= ?
sec= ?
cot= ?

*b is not 1; and c is not 3.75

Answer 1

You need an "argument" after csc and sin
e.g. csc Ø = 3.75 = 375/100 = 15/4
then sin Ø = 4/15
so that particular triangle has sides
4 , √209 , and hypotenuse 15

since I cannot tell which sides you labeled a , b, and c
other than the hypotenue is usually labeled c

I will take a stab that the side of a=3 matches the 4 of my triangle
so
3 : b : c = 4 : √209 : 15
3/4 = c/15
c = 45/4

and

b/√209 = 3/4
b = 3√209/4

(for the second part , again sin = (1/3.75) is just that, a mathematical sin)

from above
sin Ø = 4/15
cos Ø = √209/15
tan Ø = 4/√209
sec Ø = 15/√209
cot Ø = √209/4
csc Ø = 15/4 or 3.75