Çözüldü Euler's Formula for Complex Numbers - Trigonometry

For the SAT Math Subject Test, a slightly hardened version of a solved problem by the University of Florida:

Which of the following is the smallest set of complex numbers that the number below belongs to?

sin{ arctan[ e^(π·i) ] }·{ cos(7π) + i·sin[ arcsec(1) ] }

A) Nonreal Complex
B) Not a Complex number
C) Irrational
D) Rational
E) Pure Imaginary

Correct Choice: C (Irrational)

First Part:
sin{ arctan[ e^(π·i) ] } = -1 / √2
https://www.sorumvar.net/frm/konula...gonometrik-fonksiyonlar-yks-2023te-yok.12451/

Second Part:
cos(7π) + i·sin[ arcsec(1) ] = -1
(Homework for the interested students. Please let me know if any difficulty arises.)

Result: (-1 / √2)(-1) = 1 / √2.

Check by WolframAlpha:

https://i.ibb.co/CJCwyYb/Complex-WA.png
https://www.wolframalpha.com/input?i=sin{ arctan[ e^(π·i) ] }·{ cos(7π) + i·sin[ arcsec(1) ] }

Original Question:

https://i.ibb.co/wKZvgpP/UFL.png
https://academicresources.clas.ufl.edu/wp-content/uploads/sites/14/MAC-1105-Exam-1.pdf (Page 1, Question 3)
Answers: https://academicresources.clas.ufl.edu/wp-content/uploads/sites/14/MAC-1105-Exam-1-Key.pdf