```{python}
#| output: 'asis'
# Q3
from sympy import *
#pt=10
#vspace="8cm"
### q opt
opt=[
  {'fname':'csc','value':Rational(2,5)*pi},
  {'fname':'sin','value':Rational(2,9)*pi},
][ver]
### derived opt
cofn={
  'sin':'cos','cos':'sin','tan':'cot','cot':'tan','sec':'csc','csc':'sec'
}
dopt={'gname':cofn[opt['fname']]}
### answer
complement=Rational(1,2)*pi-opt['value']
lcomplement=fr"{latex(Rational(1,2)*pi)}-{latex(opt['value'])}"
latexans=fr"\{dopt['gname']}\left({latex(complement)}\right)"
solution=fr"""
:::{{.sol}}
$$\{opt['fname']}\left({latex(opt['value'])}\right)=\{dopt['gname']}\left({lcomplement}\right)=\boxed{{ {latexans} }}$$
:::
"""
### output
output=fr"\question[{pt}] "
output+=fr"""
Find a cofunction with the same value as $\{opt['fname']} {latex(opt['value'])}$. Write your answer in radians.
"""
footer= fr"""{solution}""" if showanswer else fr"""\vspace{{ {vspace} }}"""
### print
print(output,footer)
```