103 Trigonometry Problems

4. Solutions to Introductory Problems 107
It follows that [ABCDEF ]=48 √ 3.
Note: The vertices of the hexagon are A = (0, 0), B =
(
6 √ ) ( )
( )
3, 6 , D = √ 10
, 10 , E = (0, 8), and F = − √ 8 , 4 .
3 3
( )
√ 10
, 2 , C =
3
32. Show that one can use a composition of trigonometry buttons such as, sin, cos,
tan, sin −1 , cos −1 , and tan −1 , to replace the broken reciprocal button on a
calculator.
Solution: Because cos −1 sin θ = π/2 − θ, and tan(π/2 − θ) = 1/ tan θ for
0