exact values of trig functions/cofunction identities
what are some tricks to memorizing the unit circle?
-any angle over 6 is closest to x axis -QI: original fraction, QII: one less than denominator, QIII: one more than denominator, QIV: one less than 2 times denominator -all points are fractions with denominator 2 -going away from x axis, numerators go 3, 2, 1, 3, 2, 1 -all fractions have a root in the numerator
graphing secant:
-graph cosine -asymptotes at midline of cosine -curves "bounce" off min and max
graphing cosecant:
-graph sin -asymptotes at midline of sin -curves "bounce" off min and max
what are some things to look for when simplifying/ verifying trig expressions?
-put things in terms of sin/cosine -look for pythagorean identities -even/odd identities -look for ways to factor -bowtie method -separate fraction -multiply by conjugate (helps if only 1 term)
an odd trigonometric function of a negative theta= ex. sin(-x)
-sin(x)
what is the range of y values for arcsin?
-π/2, π/2
what is the range of y values for arctan?
-π/2, π/2
what is the range of y values for arccos?
0, π
one puts a coat in the closet
1 + cot^2x = csc^2x
one gets a tan by the sea
1 + tan2x = sec2x?
writing an equation based off graph
amplitude: distance from midline to min/max period: use 2π/b=length of period along x axis vertical shift: how far from 0 is the starting point on y axis horizontal shift: use periodx + c=0
an even trigonometric function of a negative theta= ex. cos(-x)
cos(x)
which trigonometric functions are even?
cosine and secant
sin (90-x) = ?
cosx
if tanx = sinx/cosx, then cotx = ?
cosx/sinx
1/tanx=
cotx (cotangent)
sec (90-x) = ?
cscx
1/sinx=
cscx (cosecant)
basics of cos parent graph
even function starting point (0,1) amplitude: 1 period: 2π dcv: π/2
basics of sin parent graph
odd function starting point (0,0) amplitude: 1 period: 2π dcv: π/2
how do you identify the period and dcv of a sin/cosine graph?
period: 2π/b dcv: period/4
1/cosx=
secx (secant)
what are the three pythagorean identities?
sin^2x + cos^2x = 1 1 + tan^2x = sec^2x 1 + cot^2x = csc^2x
what are the 3 pairs of cofunctions?
sine and cosine, tangent and cotangent, secant and cosecant
which trigonometric functions are odd?
sine, cosecant, tangent, and cotangent
basics of tan parent graph:
starting point (0,0) left asymptote: -π/2 right asymptote: π/2 no amplitude period: π dcv: π/4 (but write π/2)
basics of cot parent graph:
starting point (π/2,0) left asymptote: 0 right asymptote: π no amplitude period: π dcv: π/4 (but write π/2)
cot (90-x) = ?
tanx
what are the three ways to find the values of trigonometric functions?
the unit circle, the chart, and special right triangles
