(1) Co-Function Identities: sin( π 2 − u) = cos(u), cos( π 2 − u) = sin(u

F ORMULA S HEET
(1) Co-Function Identities:
π
π
π
sin( − u) = cos(u), cos( − u) = sin(u), tan( − u) = cot(u)
2
2
2
π
π
π
csc( − u) = sec(u), sec( − u) = csc(u), cot( − u) = tan(u)
2
2
2
(2) Periodic and Even-Odd Identities
sin(u + 2π) = sin(u), cos(u + 2π) = cos(u), tan(u + π) = tan(u)
csc(u + 2π) = csc(u), sec(u + 2π) = sec(u), cot(u + π) = cot(u)
sin(−u) = − sin(u), cos(−u) = cos(u), tan(−u) = − tan(u)
csc(−u) = − csc(u), sec(−u) = sec(u), cot(−u) = − cot(u)
(3) Sum-Difference Formulas
sin(x + y) = sin(x) cos(y) + cos(x) sin(y)
sin(x − y) = sin(x) cos(y) − cos(x) sin(y)
cos(x + y) = cos(x) cos(y) − sin(x) sin(y)
cos(x − y) = cos(x) cos(y) + sin(x) sin(y)
tan(x) + tan(y)
tan(x + y) =
1 − tan(x) tan(y)
tan(x) − tan(y)
tan(x − y) =
1 + tan(x) tan(y)
(4) Double Angle Formulas [NOTE: you have to know sin(2x) and cos(2x) formulas]
tan(2x) =
2 tan(x)
1 − tan2 (x)
(5) Power-Reducing Formulas
1 − cos(2u)
2
1
+
cos(2u)
cos2 (u) =
2
1 − cos(2u)
2
tan (u) =
1 + cos(2u)
sin2 (u) =
(6) Half Angle Formulas
r
x
1 − cos(x)
sin( ) = ±
2
2
r
1 + cos(x)
x
cos( ) = ±
2
2
x
sin(x)
1 − cos(x)
tan( ) =
=
2
1 + cos(x)
sin(x)
1
NAME:
COLLEGE ALGEBRA -ANALYTIC GEOMETRY FINAL
INSTRUCTOR: HAROLD SULTAN
1. I NSTRUCTIONS
(1) Timing: You have exactly 2 hours (120 minutes) for this exam.
(2) There are 6 questions in total, with the following scoring breakdown:
Question Total Points Your points
1
10
2
10
3
10
4
10
5
10
6
10
Total
60
(3) Please show your work and JUSTIFY all answers unless otherwise specified. Partial credit will be awarded
(4) Many of questions have multiple parts. Each question is on its own page. Please
feel free to work on the back of the page or scrap paper if necessary.
(5) Challenging Questions are marked (**)
(6) Good Luck!
Date: 12/20/10.
2