Question 8906
In order to solve these trig problems, you should remember:
sin^2X+cos^2X=1
and remember that 
tan=sin/cos
cot=cos/sin
sec=1/cos
csc=1/sin

1. sin=(sqrt3)/4 then:

cos=(sqrt13)/4
tan=(sqrt3/sqrt13)
csc=4/(sqrt3)
sec=4/(sqrt13)
cot=(sqrt13)/(sqrt3)

2. cot=1/2 then:

sin=2/(sqrt5) 
cos=1/(sqrt5)
tan=2
csc=(sqrt5)/2
sec=sqrt5
cot=1/2

3. csc=5 then:

sin=1/5
cos=(2sqrt6)/5
tan=1/(2sqrt6)
sec=5/(2sqrt6)
cot=(2sqrt6)

4. sec=5/3 then:

sin=4/5
cos=3/5
tan=4/3
csc=5/4
cot=3/4

5. cot=2 then:

sin=1/(sqrt5)
cos=2/(sqrt5)
tan=1/2
csc=sqrt5
sec=(sqrt5)/2