3b

Question 1

inverse of a function

Answer 1

the result of switching the input and output values of a function

Question 2

the output of an inverse trigonometric function will be…

Answer 2

an angle measure

Question 3

two ways to represent inverse trigonometric functions

Answer 3

1) sin^-1
2) arcsin

Question 4

why are domains of inverse trigonometric functions restricted?

Answer 4

they wouldn’t be functions without the restrictions! (wouldn’t pass the vertical line test! (normal trigonometric functions don’t pass horizontal line test))

Question 5

to have inverses, a function must pass…

Answer 5

the horizontal line test

Question 6

restricted domain of an sin function

Answer 6

[-pi/2, pi/2]

Question 7

restricted domain of an cos function

Answer 7

[0, pi]

Question 8

restricted domain of an tan function

Answer 8

(-pi/2, pi/2)

Question 9

the restricted domain of a function is the ____ of its inverse function

Answer 9

range of possible solutions

Question 10

restricted domains as shaded on unit circle

Answer 10

sin ~ Q1, Q4 (right half)
cos ~ Q1, Q2 (top half)
tan~ Q1, Q4 (right half)

Question 11

after find solutions of an inverse function…

Answer 11

double check they are in the allotted domain!

Question 12

is sin(x)=1/2 equivalent to arcsin(1/2)=x

Answer 12

No, both have pi/6 as a solution but due to the restricted domain of the inverse function that is its only solution whereas the sin function has multiple (infinite) solutions.

Question 13

since trigonometric functions are periodic…

Answer 13

they can have infinitely many solutions (if the domain is not restricted)

Question 14

general solution to sin(x)=1/2

Answer 14

x=pi/6+2pik
and
x=5pi/6+2pik
where k is any integer

Question 15

general solution to cos(x)=1/2

Answer 15

x=pi/3+2pik
and
x=5/3+2pik
where k is any integer

Question 16

general solution to tan(x)=1

Answer 16

x=pi/4+pik
where k is any integer

Question 17

general solution to all sin and cos functions

Answer 17

-find solutions for x on first rotation of unit circle
-write an equation for each with +2pik attached
-clarify k is any integer

Question 18

general solution to all tan functions

Answer 18

-find smallest solution for x on first rotation of unit circle
-write an equation with +pik attached to the solution
-clarify k is any integer

Question 19

steps to solve trig equations

Answer 19

1. isolate the trig function
2. find the corresponding angles that satisfy the equation
3. consider the domain restrictions
   –if note add pik or 2pik
4. write solutions

Question 20

REMEMBER WITH SQUARE ROOTS

Answer 20

solutions can be +/-

Question 21

(sinx)^n=

Answer 21

sin^nx

Question 22

[] vs ()

Answer 22

[] if </> or equal to (includes end values)
() if strictly </> (does not include max and min values)

Question 23

steps for solving trig inequalities

Answer 23

1. set f(x)=0 and solve
2. make a sign chart with you solutions (remember domain restrictions!)
3. test a value in each interval
4. interpret the sign chart and answer the inequality

Question 24

</> signs flip when…

Answer 24

you divide by a negative number

Question 25

secant

Answer 25

sec=1/cos

Question 26

cosecant

Answer 26

csc=1/sin

Question 27

cotangent

Answer 27

cot=1/tan=cos/sin

Question 28

Graphs of sec, csc, cot are undefined where...

Answer 28

sec, csc, tan hit x axis

Question 29

range of sec

Answer 29

(-inf, -1] [1, inf)

Question 30

graph of sec and csc

Answer 30

mini parabolas on top of maxs and mins

Question 31

undefined ares of sec graph

Answer 31

x=pi/2+pik

Question 32

range of csc

Answer 32

(-inf, -1] [1, inf)

Question 33

range of cot

Answer 33

(-inf, inf)

Question 33

undefined areas of csc graph

Answer 33

x=pik

Question 34

undefined areas of cot graph

Answer 34

x=pik

Question 35

cot graph

Answer 35

negative version of tan graph shifted over pi/2, so it fits the new asymptotes of pik

Question 36

to find asymptotes of an equation

Answer 36

plug x and the transformations that directly affect it into the "x" of the equation and solve so x is by itself

Question 37

to solve csc, cot, sec

Answer 37

isolate and change into sin, cos, tan to use unit citcle

Question 38

pythagorean identity

Answer 38

cos^2x+sin^2x=1

Question 39

you can change the pythagorean identity

Answer 39

into a lot! --even tan, if you divide by cos! --to solve for sin^2x or cos^2x

Question 40

sum and diff identities

Answer 40

sin(a+/-b)=sinacosb+/-cosasinb - sign is the same cos(a+/-b)=cosacosb-/+sinasinb - sign changes

Question 41

double angle identities

Answer 41

sin(2x)=2sinxcosx cos(2x)=cos^2x-sin^2x=1-2sin^2x=2cos^x-1

Question 42

polar coordinates

Answer 42

r, theta output, input

Question 43

y =

Answer 43

sin(theta) * r

Question 44

x =

Answer 44

cos(theta) *r

Question 45

r =

Answer 45

+/- sqrt (x^2 + y^2)

Question 46

tan(theta) =

Answer 46

y/x

Question 47

i =

Answer 47

sqrt(-1)

Question 48

complex number rectangular coordinates

Answer 48

a+bi = (a,b)

Question 49

complex number polar coordinates

Answer 49

(rcos(theta))+i(rsin(theta))

Question 50

r(theta) = asin(theta), +/- a?

Answer 50

+ ~ symmetrical to y axis on top - ~ symmetrical to y axis on bottom

Question 51

r(theta) = acos(theta), +/- a?

Answer 51

+ ~ symmetrical to x axis on right - ~ symmetrical to x axis on left

Question 52

if b is even...

Answer 52

graph will have 2 b petals

Question 53

if b is odd...

Answer 53

graph will have b petals

Question 54

if r is positive and increasing, the distance between r and the origin is...

Answer 54

increasing

Question 55

if r is negative and decreasing, the distance between r and the origin is...

Answer 55

increasing

Question 56

if r is positive and decreasing, the distance between r and the origin is...

Answer 56

decreasing

Question 57

if r is negative and increasing, the distance between r and the origin is...

Answer 57

decreasing

Question 58

relative extrema occur

Answer 58

when graph changes from increasing to decreasing or vice versa

Question 59

AROC of a polar function

Answer 59

y2-y1/x2-x1 indicates the rate at which the radius is changing per radian

Question 60

estimating with AROC

Answer 60

f(x) = known y + AROC (x-known x)