Challenging trigonometry problems

See Sal solve a bunch of very challenging geometry and algebra problems that involve trigonometry.

Trig challenge problem: area of a triangle

Trig challenge problem: area of a hexagon

Trig challenge problem: cosine of angle-sum

Trig challenge problem: arithmetic progression

Trig challenge problem: maximum value

Trig challenge problem: multiple constraints

Trig challenge problem: system of equations