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