Question

help

Answer 1

@Vocaloid

Answer 2

@Vocaloid

Answer 3

use the second angle identity to find cos(75) by letting theta = 150 degrees

Answer 4

cos 75=.258

Answer 5

we are looking for an exact value so we cannot just plug this into a calculator, you have to go through the formula + calculations.

Answer 6

b?

Answer 7

well done

Answer 8

2?

Answer 9

for #2? I think so, technically identity 1 would work but I think 2 is closer to what they want

Answer 10

as a hint for #3, you can re-write the product and put sin and cos together

Answer 11

is it d

Answer 12

for 2

Answer 13

3 give me a minute

Answer 14

c? c and almost look identical lol

Answer 15

d

Answer 16

good, D, the difference is where the 2 is wrt theta

Answer 17

is 2 d ?

Answer 18

for #2 I'm not 100% sure, C and D seem too far from what the identity needs, I was between A and B sort of leaning towards B? :S

Answer 19

oh ok b it is then you're the genius I try lol

Answer 20

you were right

Answer 21

can you help with more

Answer 22

I'll try

Answer 23

for 1) you just have to know the definitions of the functions, for example tan(theta) is sin/cos not the other way around, so check 1 is not marked off

keep going with the other possibilities, eliminating the ones that are not mathematically correct

Answer 24

those are the identities i can probably find it

Answer 25

b is one

Answer 26

good, there's one more, it's pretty easy to find once you look at the csc and sec definitions

Answer 27

csc = 1/sin
sec = 1/cos

based on this which one(s) can you eliminate?

Answer 28

both because both in answer choices are wrong lol

Answer 29

good so it's just B + the last choice

Answer 30

is sec tan /sin

Answer 31

number 2?

Answer 32

if you re-write tan as sin/cos then

sec = (sin/cos)/sin, then the sins cancel out and you get 1/cos which is equal to sec

Answer 33

anyway, for 2: I'm not 100% sure but we could at least eliminate a few choices that aren't helpful, like the first one probably isn't helpful since we're dealing with cot and sec in separate parts of the fraction

Answer 34

my best (?) guess would be to re-write everything in terms of tan, you'd use identifies B and D to do that :S so those two?

Answer 35

I trust your answer so we'll go with it lol

Answer 36

notice how he replaced sec^2 with 1/(sin^2) what do you think is the problem with that?

Answer 37

doesn't cos with sec not sec and sin

Answer 38

b lol

Answer 39

good, so sec^2 isn't 1/sin^2 it's 1/cos^2 making the error in answer choice B, well done

Answer 40

a?

Answer 41

for Albert's proof, C and D are factually incorrect so we immediately eliminate these

you're on the right track, but he's already done tan(theta) = sintheta/costheta, he has to do something else to make the left side equal to the right side

Answer 42

if he re-writes that cos as cos^2 / cos then he can also re-write sec as 1/cos, giving them all common denominator cos, so B

Answer 43

6 is a

Answer 44

as a hint, cos^2 = 1 - sin^2 so what would we need to do to make the denominator 1 - sin^2 instead of 1 - sin?

think back to algebra, difference of squares

Answer 45

multiply

Answer 46

good but multiply by what?

Answer 47

A^2 - B^2 = (A+B)*(A-B)
1^2 - sin^2 = ____ * (1-sin)

fill in the blank

Answer 48

is answer d?

Answer 49

good, you'd multiply by 1 + sin following the rule, so D

Answer 50

6 is a

Answer 51

for 7, use the tan sum identity, treat "alpha" as x1 and "beta" as (x1+x2)

Answer 52

yeah 6 is a that's just a quick calculation check

Answer 53

b?

Answer 54

check the sign in the numerator, notice how it's positive

Answer 55

c

Answer 56

see how we plugged in x2 + x3 for beta, and how tan(x2+x3) has to keep x2 and x3 in parentheses?

Answer 57

oh its d okay same set up but different symbol ok

Answer 58

yup good

Answer 59

have to re-write cos(3x) as cos(2x + x) then use the cos sum formula to expand cos(3x)

Answer 60

cos(A+B)=cosAcosB−sinAsinB

where A is 2x and B is x, then after that you need to keep expanding until you get something that looks like one of the choices

Answer 61

b

Answer 62

can you show me your calculations? still working on it myself

Answer 63

honestly mathway said that well something close to it it gave me an odd cal

Answer 64

I'll just get back to 8, I can't figure out the calculation yet

anyway for 9 you just want to use the half angle formula to calculate sin(theta/2) where theta = 45

Answer 65

please at least attempt the calculations

Answer 66

a

Answer 67

you're getting there but that's just the sin value, since the force is mg sin theta you must multiply the result from A by m and g (given in the problem so what do you get?)

Answer 68

c

Answer 69

m * g = 0.01 * 9.8 = 0.049/2

combine this with what we got from before

Answer 70

oh ok I think I got it maybe but d is the answer

Answer 71

we got sintheta = sqrt(2 - sqrt(2))/2

multiply this with 0.049 * 2

what do you get?

Answer 72

so the denominator is multiplied ? does that mean the answer is b kinda lost on this topic but am attempting

Answer 73

anyway, yeah it's B, I finally figured out # 8 so we can get back to that

Answer 74

okay thank you for hwlping I know I'm annoying

Answer 75

anyway, for cos(3x) we can split this into cos(2x + x)

using the cos addition formula we get:

Answer 76

plugging 2x for alpha and x for beta

cos(2x)cos(x) - sin(2x)sin(x)

all of that goes over cos(x) sin(x) so we write it like:

Answer 77

we can split this fraction into two fractions like so:

Answer 78

we can cancel out common units like so:

Answer 79

anyway, if you remember our definitions of csc and sec from before, you can re-write these in terms of csc and sec, what would be your final answer?

Answer 80

does this make it a little more clear to see how it can be re-written in terms of sec and csc?

Answer 81

yes b and c are the only ones written in that form

Answer 82

substituting csc for 1/sin and sec for 1/cos

gives us

cos(2x)csc(x) - sin(2x)sec(x) answer choice A

Answer 83

anyway I still gotta think about #10, I know A is nonsense so it's out

Answer 84

last question and then i'll try and figure the other out if not i'll be back

Answer 85

cos^(theta) = [ 1 + cos(2theta) ] /2

if we replace "theta" with "2theta" we get

cos^(2theta) = [1 + cos(4theta) ] / 2 making the first answer choice the only one that is mathematically valid

Answer 86

for 10 or 11

Answer 87

11

Answer 88

sorry doing math and art history at the same time if you know an art history genius please let me know lol

Answer 89

anyway, for 10, I am not 100 on this but since we have tan(3theta) not tan(2theta) using the double angle formula would result in a tan(3theta/2) term which gets us "stuck" so C

Answer 90

anyway I hope that helps, sorry if there are any errors it's past midnight and I'm kind of burnt out

Answer 91

I'll ask around for art history

Answer 92

okay thank you and it's okay better than I would've gotten