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