Question

Use an addition or subtraction formula to find the exact value of the expression.

tan(-5pi/12)
sin(23/12)
cos(13pi/12)

Answer 1

Please help!

Answer 2

it wants you to seperate the "radian" given into known radians that you can play with

Answer 3

like pi/3 pi/4 pi/6 pi/ 2pi those things

Answer 4

3 and 2 = 5..... lets try that on the first one

Answer 5

OK

Answer 6

a=-3pi/12 b=2pi/12

a = -pi/4 b = pi/6

Answer 7

still remember the addition stuff for tangent?? =D

Answer 8

Kind of

Answer 9

tana + tanb
--------- ;)
1 - tanatanb

Answer 10

but we is subtracting here.... or adding if you wanna get too technicalized about it

Answer 11

lets add....i wanna add :)

Answer 12

tan(-pi/4) + tan(-pi/6)
---------------------
1 - tan(-pi/4) tan(-pi/6)

Answer 13

lets add :)

Answer 14

where did u get all of these numbers from

Answer 15

-1 + -sqrt(3)/3
-----------------
1 - (-1)(-sqrt(3)/3)

Answer 16

Huh?

Answer 17

-5pi -3pi -2pi
---- = ---- + ---- right?
12 12 12

Answer 18

yes

Answer 19

goos, the reduce those 2 new radians to something we can use: something familiar..

-pi/4 and -pi/6

Answer 20

tan(-pi/4) = -1 its a 45 degree line with a negative slope

tan(-pi/6) = -30degrees = -1/sqrt(3) = sqrt(3)/3

Answer 21

-1 + -sqrt(3)/3
---------------
1 - (-1)(-sqrt(3)/3)

Answer 22

ok

Answer 23

-1 - sqrt(3)/3 -3 - sqrt(3)
------------ = ----------- we can rationalize the
1 - sqrt(3)/3 3 - sqrt(3) denominator maybe :)

Answer 24

-3 - sqrt(3) (3+sqrt(3)) -12 -6sqrt(3)
----------- --------- = -------------
3 - sqrt(3) (3+sqrt(3)) 6


reducing we get: -2 -sqrt(3) if I did it right in me head

Answer 25

yes

Answer 26

yes im right? or yes if we agree theyll shut up? :)

Answer 27

um... both

Answer 28

lol .... i got enough voices in me head that we aint gonna shut up regardless lol

Answer 29

lol

Answer 30

sin(23/12) is this missing a pi?

Answer 31

ok so, the answer for the first one is -2sqrt3

Answer 32

no its: (-2) - (sqrt(3))

Answer 33

Yes, it is. It is sin(23pi/12)

Answer 34

23 is almost 24; so were looking at 2pi - pi/12 at that one. but pi/12 aint in our "easy" angles so we gotta look harder for an answer

Answer 35

ok

Answer 36

why r u rounding up to 24?

Answer 37

just looking at where the angle ends up; its tucked under the 2pi.

23pi/12 = 20pi/12 + 3pi/12

Answer 38

20pi/12 = 5pi/3

3pi/12 = pi/4

Answer 39

these are angles we know about, so we can use these

Answer 40

ok

Answer 41

sin(23pi/12) = sin(5pi/3 + pi/4)

sin(a+b) = sin(a)cos(b)+sin(b)cos(a)

Answer 42

sin(5pi/3) = -sqrt(3)/2
cos(5pi/3) = 1/2

sin(pi/4) = cos(pi/4) = 1/sqrt(2)

Answer 43

is the answer [sqrt3-1]/ [2sqrt2]

Answer 44

sin(a+b) = (-sqrt(2)/2) (1/sqrt(2)) +(1/sqrt(2))(1/2)

Answer 45

-2/4 + sqrt(2)/4 = sqrt(2)-2
--------
4

Answer 46

ack!!...i typoed that up didnt I

Answer 47

yes

Answer 48

(-sqrt(3)/2) (1/sqrt(2)) +(1/sqrt(2))(1/2)

-sqrt(6)/4 + sqrt(2)/4 = sqrt(2) - sqrt(6)
--------------
4

Answer 49

that should be correct :)

Answer 50

let's see...

Answer 51

im going for coffee......like a bad little mormon :)

Answer 52

Correct!

Answer 53

haha...

Answer 54

have we done the third one?

Answer 55

theres a third one? and the watering hole is getting refilled .....

Answer 56

you* sorry for taking the credit :P

Answer 57

It is cos(13pi/12)

Answer 58

your like my conscinece....that is if I had a consicence lol

Answer 59

pi/12 = 15 degrees. I knew it!!

Answer 60

this is 225 - 30 degrees.... or 5pi/4 - pi/6

Answer 61

cos(a-b) - cos(a)cos(b) + sin(a)sin(b)

Answer 62

sin and cos 5pi/4 = -1/sqrt(2) (a)
sin 30 = 1/2 cos30 = sqrt(3)/2

Answer 63

How the hell do you know all of this?

Answer 64

(-1/sqrt(2)) (sqrt3)/2) + (-1/sqrt(2)) (1/2)

-sqrt(6)/4 + -sqrt(2)/4 = -sqrt(6) -sqrt(2)
--------------
4

Answer 65

I know nutheeeng!!

Answer 66

kidding me

Answer 67

col. klink right?

Answer 68

can u help me with more? PLEASEEEEEEE:)

Answer 69

was I right?

Answer 70

Oh yeah....

Answer 71

how am i supoosed to increase my fan numbers if I only help one person?......lol, like that matters HAH!!; yeah, I can help with what I can;)

Answer 72

THANK YOU SO MUCH!!!

Answer 73

its all about the benjamins baybay lol

Answer 74

Use an addition or subtraction formula to find the exact value of the expression.

Tan(-15degrees)

Answer 75

yep

Answer 76

sin juice is sitting on the table again; brb....

Answer 77

ok

Answer 78

the tan(-15) degrees = tan(-pi/12) = tan(23pi/12)

Answer 79

lets go with 45 - 30; cause 15 = pi/12

Answer 80

Use an addition or subtraction formula to write the expression as a trigonometric function of one number, and then find its exact value.

cos (17pi/21) cos (-pi/7) - sin (17pi/21) sin (-pi/7)

This is gibberish to me :'(

Answer 81

ok

Answer 82

im gonna guess that the tan(-15) = -sqrt(3)/6 but let me verify that with my sources ;)

Answer 83

you're your own source lol

Answer 84

it's wrong, my hw program says it's wrong

Answer 85

I aint verified it yet....hold on lol

Answer 86

tan(45) = 1 ; tan(30) = 1/sqrt(3)

tan(45-30) =

tan(45) - tan(30)
---------------
1 + tan(45)tan(30)

1 - sqrt(3)/3 (1-sqrt(3)/3)
----------- -----------
1 + sqrt(3)/3 (1-sqrt(3)/3)

Answer 87

ok

Answer 88

1 -2sqrt(3)/3 + 3/9
------------------
1 - 3/9

Answer 89

9 -6sqrt(3) + 3
-----------
9
-------------
9-3
---
9

Answer 90

9 -6sqrt(3) + 3 12 -6sqrt(3)
------------- = ----------- = 2 -sqrt(3)
9-3 6

but thats (15) degrees, we need to negate it

-1(2 -sqrt(3)) = sqrt(3) - 2

Answer 91

Righto... :)

Answer 92

i read it in the stars lol

Answer 93

Use an addition or subtraction formula to write the expression as a trigonometric function of one number, and then find its exact value.

cos (17pi/21) cos (-pi/7) - sin (17pi/21) sin (-pi/7)

This is gibberish to me :'(

Answer 94

haha...

Answer 95

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

they give you "a" and "b" so....

cos(17pi/21 + -pi/7)

cos(17pi/21 -3pi/21) = cos(14pi/21) = cos(2pi/3) or cos(120) degrees

Answer 96

cos(120) = -1/2

Answer 97

how do you get cos120 = -1/2

Answer 98

how? cause 120 degree is in Q2 were cos is negative.

so just take the reference angle of cos(60) and negate it.

cos(60) = 1/2; cos(120) = -1/2