The document discusses four math problems involving trigonometric identities, permutations, logarithms, and conic sections. Specifically, it provides worked examples to: 1) Prove a trigonometric identity by using double angle identities and reducing both sides of the equation. 2) Calculate the number of possible concert schedules that can be created from a list of provinces using permutations. 3) Determine which used car dealer offers the cheapest Honda Civic after 3 years of depreciation by using logarithms. 4) Derive the equations of an ellipse and parabola that can model a tunnel arch and determine which model more closely approximates the actual height at a given point.

1. Problem no.1 Trig Identities

8. Problem no. 2 Permutations

9. I’m J.r. Manleigh and I am the manager of the new band called “Private”. I have here the list of the possible provinces that we can have the concert. Pangasinan Bataan Bukidnon Leyte Batangas Sulu Romblon La Union Surigao Del Norte Bohol Cavite Surigao Del Sur Cebu Laguna Mindanao(green) Visayas(yellow) Luzon(red)

21. Problem no. 4 Conics

22. What you see above is a tunnel in Winnipeg that has a length of 162 m and a height of 56 m.