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