exam 3

Question 1

basic unit circle values

Answer 1

x^2+y^2=1
π/6 (√3/2, 1/2)
π/4 (√2/2, √2/2)
π/3 (1/2, √3/2)

Question 2

log properties

Answer 2

loga1= 0
logaA= 1
logaA^x=x
a^logaX= x
logaA^c= ClogaA
loga(AB) = logA+logB
loga(A/B)= logA-logB

Question 3

exponential and log equations steps

Answer 3

1) put exponential on one side

2) solve

Question 4

trig functions

Answer 4

sin^2(x) + cos^2(x)= 1
tan^2(x)+1=sec^2(x)
1+cot^2(x)=csc^2(x)

Question 5

degrees to radians

Answer 5

multiply π/180

Question 6

radians to degrees

Answer 6

multiply 180/π

Question 7

coterminal angles

Answer 7

add or subtract 2π (360 degrees) to given angle

Question 8

trig functions of angles

Answer 8

SOH CAH TOA

a^2+b^2=c^2

Question 9

basic trig function domain and range

Answer 9

sin(θ)

domain: (-∞,∞)
range: [-1,1]

cos(θ)

domain: (-∞,∞)
range: [-1,1]

tan(θ)

domain: (-∞,∞) {π/2+nπ}
range: (-∞,∞)

Question 10

inverse trig functions

Answer 10

sin-1(θ)

domain: [-1,1]
range: [-π/2, π/2]

cos-1(θ)

domain: [-1,1]
range: [0, π]

tan-1(θ)

domain: (-∞,∞)
range: (-π/2, π/2)

Question 11

cancellation property

Answer 11

f(f^-1(x))= x
f^-1(f(x))=x
*anything >1 is undefined

Question 12

even-odd identities

Answer 12

sin(-x)= -sinx 
cos(-x)= cosx
tan(-x)= -tanx

Question 13

guidelines for proving trig identities

Answer 13

1) start with one side
* indicate which side u choose to start with
2) use known identities
3) covert to sines and cosines

Question 14

formula for sine

Answer 14

sin(x+y)= sinXcosY + cosXsinY

sin (x-y)= sinXcosY - cosXsinY

Question 15

formula for cosine

Answer 15

cos(x+y)= cosXcosY - sinXsinY
cos(x-y)= cosXcosY - sinXsinY

Question 16

double-angle formulas

Answer 16

sine: sin2x= 2sinxcosx
cosine: cos2x= cos^2x-sin^2x
= 1-2sin^2x
= 2cos^2x-1
tangent: tan2x=sin2x/cos2x

Question 17

sine graph

Answer 17

sink(x-b)+c
period: 2π/k
amp: IaI 
phase shift: b
d=period/4
*always starts with "b"
*basic graph starts from 0

Question 18

cosine graph

Answer 18

acosk(x-b)+c
period: 2π/k
amp: IaI 
phase shift: b
d=period/4
*always starts with "b"
*basic graph starts at highest point

Question 19

tangent graph

Answer 19

atank(x-b)+c
period: π/k
d=period/4
*b in the middle
*2 asymptotes at the very ends

Question 20

basic trig equation steps

Answer 20

1) find primary solution in one complete period
sin [0,2π) cos [0,2π) tan (-π/2, π/2)
2) find general solution by adding the solution in step 1 by the multiple of the period
*sin and cos: add 2kπ
*tan: add kπ

Question 21

5-step strategy

Answer 21

1) write down in one function of one angle
2) find values of written function
3) solve for angle
4) solve for variable
5) check restrictions

Question 22

basic trig equations CHECK

Answer 22

1) factor
2) identities
3) formulas
- addition/subtraction
- double angle
* u substitution

Question 23

if inverse function is on the outside, look at the

Answer 23

domain

Question 24

if inverse function is on the inside, look at the

Answer 24

range

Question 25

solving exponential/log equations: exponential

Answer 25

1) isolate exp
2) take loga
3) solve for variable
* no check
* sometimes we can factor

Question 26

solving exponential/log equations: log

Answer 26

way 1) 
1. isolate loga
2. write in exp form 
3. solve for variable 
4. check 
way 2)
logaX=logaY; X=Y