Trigonometry





NEW TRIG NOTES including: >degree to radian conversion process >determining sin, cos, tan, and their reciprocals using special triangles >trigonometric transformations [|Trigonometry.doc]

Here is the GSP doc. containing the function outlined in the previous document: [|trig1.gsp]

When graphing transformations of sin/cos waves, remember the shrotcuts: >draw in dotted lines indicating new period, new amplitude (transformed), as well as new middle line >transform important points first (those which normally fall on the x-axis or at max/min's of wave's amplitude) then fill in the rest

TRIG PROBLEMS (ferris wheels + tidal waves!!)

Here is a word document w/ problems + solutions:[|TRIG2.doc] Here is the GSP doc. w/ accompanying graphs (they are all contained in the document but on separate pages, look to the bottom of the first page to find little boxes with the other page numbers to find the rest of the graphs):[|trig problems 2.gsp]


 * Trigonometric Identities: **
 * Reciprocal identities:**

sin x = 1/csc x csc x = 1/sin x

cos x = 1/sec x sec x = 1/cos x

tan x = 1/cot x cot x = 1/tan x


 * Pythagorean Identities:**

Sin^2 x + cos^2 x = 1 tan^2 x + 1 = sec ^2 x cot^2 x + 1 = csc^2 x

Double angle identities:

sin2x = 2 sin x cos x cos2x = cos^2 x - sin^2 x = 2cos^2 x - 1 = 1 - 2sin^2 x

sin(A+B) = sinAcosB + cosAsinB cos(A+B) = cosAcosB - sinAsinB sin(A-B) = sinAcosB - cosAsinB cos(A+B) = cosAcosB + sinAsinB

Strategies for solving trig. Identities. > solve most complicated side > Factoring > Multiply by conjugate > Look for reciprocals > Use pythagorean or double angle identities.