As a sophomore student, I want to create 5 exercises

As a sophomore student, I want to create 5 exercises. The first one is on solving trigonometric equations, the second one is for vector applications, the third one is for parametric equation, the fourth one is for modeling periodic motion, the fifth one is for conic section. I want each exercise to contain a specific theme.

Permitted theme:

Music/Sound • Dance • Planes/Flying• Basketball • Soccer • Running • Boating • Cars/Driving • Ocean/Water/Waves • Space/Planets/Rocket/Astronauts 

And I want to have The detailed step-by-step solution to the problem created