math test study 5.5-5.6 NOW INCLUDING: 5.7 & 5.8
how many asymptotes are there in one period of csc or sec
3
REMEMBER TO FACTOR OUT B BEFORE FINDING PHASE SHIFTS
OKAY
cos -1 range
[0,pi]
which quadrants is cos -1?
first and second
how does csc x look at zero
goes up
how find amplitude of cot or tan from graphs
halfway between 0 and asymptote y value should be 1 or neg one. if it's something else that's ur asymptote.
what is the formula for amplitude
high-low/2
DRAW A RIGHT TRIANGLE IF U CAN 4 THEM BEARING PROBLEMS
ik
remember to label THE RIGHT PARTS with the right number
ik
which side is up for a positive cot graph
left side
how would you solve the system of equations : { tan (33.3) = y/x {tan(25.6) = y/(354 +x)
multiply by x and 354 +x on both sides, then set the two equal to each other, then multiply it out -- simplify -- then bring the two x sides onto the same side, then factor out x, then divide and consequently isolate x. Then plug into a calc.
what is the amplitude of cot x
none
which side does positive tan x rise to
right
how does sec(x) look at zero
starts at 1, (halfway), goes up. Next curve is down
what are pd and fr relationship
they're reciprocals
how are the graphs of f(x) and it's inverse symmetric
w/ respect to the line y=x
tan -1 ( tan x ) x IF ...
x is between ( -pi/2, pi/2)
sin -1 (sin x) = x IF....
x is between -pi/2 and pi/2 BUT... you can often find a similar angle with the same sin which works.
cos(cos -1 x) = x IF...
x is between [-1,1]
sin(sin-1 x) = x IF....
x is between [-1,1]
cos -1 (cos x) = x IF...
x is between [0, pi]
what is the a b c d form of a sin function
y=asin(b(x-c)) +d
what's the range of inverse tan
( -pi/2, pi/2) BUT THEY'RE ASYMPTOTES SO NO INCLUSIOn
what's the range of csc x and sec x
(-infinity, -1] u [1, infinity)
domain of arc tan
(-infinity, infinity)
what are the basic sec x points
-pi/2, und 0,1 pi/2,und pi,-1 3pi/2, und etc
What are tan x points
-pi/2,und -pi/4,-1 0,0 pi/4,1 pi/2,und 3pi/4,-1 pi,0 5pi/4,1 3pi/2,und
what is tan -1 of 0, _/3/3, _/3, and 1,
0, pi/6, pi/3, and pi/4
what are the basic sin x points for graphing
0,0 pi/2,1 pi,0 3pi/2, -1 2pi,0 5pi/2, 1 3pi,0 7pi/2,-1 4pi,0
what are the basic cos x points
0,1 pi/2,0 pi,-1 3pi/2,0 2pi,1 5pi/2,0 3pi,-1 7pi/2,0 4pi,1
csc x graph points
0,und pi/2,1 pi,und 3pi/2,-1 2pi,und etc.
what is the period of one cycle for sin x
2pi
what is the formula for period
2pi/b
what's the amplitude of csc x
NONE
is amp always pos or neg
POSITIVE
tan(tan -1 x) = x if...
THERE IS NO IF THERE IS ONLY ALWAYS
what is the domain of cot x
X DOES NOT EQUAL PI * N, N ELEMENT Z
cos -1 domain
[-1,1]
what is the domain of sin -1
[-1,1]
what is the range of sin x
[-1,1]
what is the range of sin -1
[-pi/2, pi/2]
what three values are the same for sin or cos
a, b, and d-- phase shift is the only altered one
what is amplitude
a-- distance from midline
what is the units for fr for simple harmonic motion
cycles/unit of time
what direction does a positive cos graph go first
down from 1
how do you find the equations for a csc or sec graph
draw in the sin or cos function and use those values
which quads is tan inverse in
first and 4th like #sin
REMEMBER WHEN WRITING CSC OR SEC EQUAtiON FROM A GRAPH THAT ThERE MAY BE A VERTICAL SHIFT IN WHICH CASE THE MIDLINE IS SHIFTED
ik
remember if the bearing is from a point not in the middle of the compas thingy then the bearing is from THAT point -- NOT the middle -- BE CAREFUL
ik
what is the range of cot and tan x
neg infin to infin
what is the domain of sin x
neg infinity to infinity
what is the domain and range of cos x
neg infinity to infinity, and [-1,1]
what is b
num of cycles from 0-2pi
what are cotangent points
o,und pi/4,1 pi/2,0 3pi/4,-1 pi,und 5pi/4,1 3pi/2,0 7pi/4,-1 2pi,und
what is sin -1 of _/3 /2
pi/3
what is the period of cot
pi/b-- so pi
what quadrants can sin -1 be in
quad 1 (positively) and quad 4 (negatively)
solve sin(cos -1 4/5)
u would draw the picture and then solve 4 the other side values and u have it
what is sin-1 (-5/2)
undefined because it is not in the domain (not between -1 and 1)
what is the unit for pd for simple harmonic motion
units of time/cyxle
what direction does a positive sin graph go first
up from 0
what's the domain of csc x
x DOES NOT EQUAL Pi*n, n is an element of the integers
what is the domain of tan x
x does not equal -pi/2 + pi*n, n e Z
what is the domain of basic sec x
x does not equal -pi/2 + pi*n, n is an element of Z
