cofunction identities
ratio(pi/2-x)=cofunc ratio
sum of cubes
SOAP
(a+b)(a^2-ab+b^2)
factor types
GCF, quadratic, difference of squares, sum/difference of cubes, grouping
exponents can vary in
fundamental identities but not in pythagorean
steps to prove an identity
- show that one side of the identity can be simplified so it is identical without moving things from one side to the other
- usually start with the more complicated side
- no specific steps
- easy to follow manner
if theres +/- 1
change to difference of squares, not cancelling exponents
dont need to rationalize in
finding exact value of ratiox
double angle formulas used to
find exact values and verify identities
square root use
+/-
trig identities work for
any value of x that is in the domain of the functions involved
if a specific interval is given
you do not need to add the infinite number of periods
multiple angle identities
use the horizontal shrink to find solutions
calculator mode
radians
do + numbers of pis to find
other appropriate quadrants
finding Q2, Q3, Q4
pi -, pi +, 2pi -
squared with odd/even
factor first
function period vs solution spacing
equation’s solutions repeat every pi or 2pi even though functions have 2pi period
sin value appears in [0, 2pi)
each distinct solution try for 2pi
steps to finding in solution (-pi, pi)
- find reference angle
- determine which quadrants are +/-
- convert angles >pi to negative by subtracting 2pi until inside
convert sin negative angles to [-pi, pi)
use reference angles in negative quadrants
finding exact value of ratio-x
use even/odd to take sing out and solve normally do not make negative inside
