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Mathematics 55 Online
OpenStudy (anonymous):

Use an addition or subtraction formula to find the exact value of the expression. tan(-5pi/12) sin(23/12) cos(13pi/12)

OpenStudy (anonymous):

Please help!

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

OK

OpenStudy (amistre64):

a=-3pi/12 b=2pi/12 a = -pi/4 b = pi/6

OpenStudy (anonymous):

still remember the addition stuff for tangent?? =D

OpenStudy (anonymous):

Kind of

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (amistre64):

lets add....i wanna add :)

OpenStudy (amistre64):

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

OpenStudy (anonymous):

lets add :)

OpenStudy (anonymous):

where did u get all of these numbers from

OpenStudy (amistre64):

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

OpenStudy (anonymous):

Huh?

OpenStudy (amistre64):

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

OpenStudy (anonymous):

yes

OpenStudy (amistre64):

goos, the reduce those 2 new radians to something we can use: something familiar.. -pi/4 and -pi/6

OpenStudy (amistre64):

tan(-pi/4) = -1 its a 45 degree line with a negative slope tan(-pi/6) = -30degrees = -1/sqrt(3) = sqrt(3)/3

OpenStudy (amistre64):

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

OpenStudy (anonymous):

ok

OpenStudy (amistre64):

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

OpenStudy (amistre64):

-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

OpenStudy (anonymous):

yes

OpenStudy (amistre64):

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

OpenStudy (anonymous):

um... both

OpenStudy (amistre64):

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

OpenStudy (anonymous):

lol

OpenStudy (amistre64):

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

OpenStudy (anonymous):

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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

ok

OpenStudy (anonymous):

why r u rounding up to 24?

OpenStudy (amistre64):

just looking at where the angle ends up; its tucked under the 2pi. 23pi/12 = 20pi/12 + 3pi/12

OpenStudy (amistre64):

20pi/12 = 5pi/3 3pi/12 = pi/4

OpenStudy (amistre64):

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

OpenStudy (anonymous):

ok

OpenStudy (amistre64):

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

OpenStudy (amistre64):

sin(5pi/3) = -sqrt(3)/2 cos(5pi/3) = 1/2 sin(pi/4) = cos(pi/4) = 1/sqrt(2)

OpenStudy (anonymous):

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

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

yes

OpenStudy (amistre64):

(-sqrt(3)/2) (1/sqrt(2)) +(1/sqrt(2))(1/2) -sqrt(6)/4 + sqrt(2)/4 = sqrt(2) - sqrt(6) -------------- 4

OpenStudy (amistre64):

that should be correct :)

OpenStudy (anonymous):

let's see...

OpenStudy (amistre64):

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

OpenStudy (anonymous):

Correct!

OpenStudy (anonymous):

haha...

OpenStudy (anonymous):

have we done the third one?

OpenStudy (amistre64):

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

OpenStudy (anonymous):

you* sorry for taking the credit :P

OpenStudy (anonymous):

It is cos(13pi/12)

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

How the hell do you know all of this?

OpenStudy (amistre64):

(-1/sqrt(2)) (sqrt3)/2) + (-1/sqrt(2)) (1/2) -sqrt(6)/4 + -sqrt(2)/4 = -sqrt(6) -sqrt(2) -------------- 4

OpenStudy (amistre64):

I know nutheeeng!!

OpenStudy (anonymous):

kidding me

OpenStudy (amistre64):

col. klink right?

OpenStudy (anonymous):

can u help me with more? PLEASEEEEEEE:)

OpenStudy (amistre64):

was I right?

OpenStudy (anonymous):

Oh yeah....

OpenStudy (amistre64):

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;)

OpenStudy (anonymous):

THANK YOU SO MUCH!!!

OpenStudy (amistre64):

its all about the benjamins baybay lol

OpenStudy (anonymous):

Use an addition or subtraction formula to find the exact value of the expression. Tan(-15degrees)

OpenStudy (anonymous):

yep

OpenStudy (amistre64):

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

OpenStudy (anonymous):

ok

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

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 :'(

OpenStudy (anonymous):

ok

OpenStudy (amistre64):

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

OpenStudy (anonymous):

you're your own source lol

OpenStudy (anonymous):

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

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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)

OpenStudy (anonymous):

ok

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

Righto... :)

OpenStudy (amistre64):

i read it in the stars lol

OpenStudy (anonymous):

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 :'(

OpenStudy (anonymous):

haha...

OpenStudy (amistre64):

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

OpenStudy (amistre64):

cos(120) = -1/2

OpenStudy (anonymous):

how do you get cos120 = -1/2

OpenStudy (amistre64):

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

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