Chapter 6 - Trigonometric Formulas and Equations

tricky things to remember

for solving these problems

half angle formulas (sin cos tan)

plus or minus depending on quadrant double x/2 to plug in for x in the formulas

when equations are in the form sin(Bx) or cos(Bx)

set inside equal to solution, then solve for x

finding x intercepts and using identities

simply set formula equal to zero, and using identites when easier

note

solve over TWO periods! example

geometry fact!

surprise! anterior angle equals sum of these two angles (adjacent angles?)

remember from algebra

taking the square root gives you two anseweres (+) and (-)

solving trig equations (sin cos example)

two solutions, and infinitely many solutions

the challenge is solving the problems

watch out for quadrants for X and Y, use triangles or identities(preferred bc faster) when necessary, recognize patterns (lots of examples on 6.1 notes)

double angle formulas (sin cos tan)

derived from sum and difference formulas sec csc and cot and just these identities over one

complex equation example

don't forget using the correct period for infinitly many solutions to sin(Bx) type equations!

Sum and Difference formulas (sin cos and tan)

easy part

solutions with arcsin

arcs have +/- answers. subtract arcs from pi for the second answer. Don't forget to account for the correct period.

cos double angle notes:

can be written different ways with pythagorean identities

note

cant cancel cosx, subtract and set equal to zero and solve instead