anonymous
  • anonymous
Use an addition or subtraction formula to find the exact value of the expression. tan(-5pi/12) sin(23/12) cos(13pi/12)
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Please help!
amistre64
  • amistre64
it wants you to seperate the "radian" given into known radians that you can play with
amistre64
  • amistre64
like pi/3 pi/4 pi/6 pi/ 2pi those things

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

amistre64
  • amistre64
3 and 2 = 5..... lets try that on the first one
anonymous
  • anonymous
OK
amistre64
  • amistre64
a=-3pi/12 b=2pi/12 a = -pi/4 b = pi/6
anonymous
  • anonymous
still remember the addition stuff for tangent?? =D
anonymous
  • anonymous
Kind of
amistre64
  • amistre64
tana + tanb --------- ;) 1 - tanatanb
amistre64
  • amistre64
but we is subtracting here.... or adding if you wanna get too technicalized about it
amistre64
  • amistre64
lets add....i wanna add :)
amistre64
  • amistre64
tan(-pi/4) + tan(-pi/6) --------------------- 1 - tan(-pi/4) tan(-pi/6)
anonymous
  • anonymous
lets add :)
anonymous
  • anonymous
where did u get all of these numbers from
amistre64
  • amistre64
-1 + -sqrt(3)/3 ----------------- 1 - (-1)(-sqrt(3)/3)
anonymous
  • anonymous
Huh?
amistre64
  • amistre64
-5pi -3pi -2pi ---- = ---- + ---- right? 12 12 12
anonymous
  • anonymous
yes
amistre64
  • amistre64
goos, the reduce those 2 new radians to something we can use: something familiar.. -pi/4 and -pi/6
amistre64
  • amistre64
tan(-pi/4) = -1 its a 45 degree line with a negative slope tan(-pi/6) = -30degrees = -1/sqrt(3) = sqrt(3)/3
amistre64
  • amistre64
-1 + -sqrt(3)/3 --------------- 1 - (-1)(-sqrt(3)/3)
anonymous
  • anonymous
ok
amistre64
  • amistre64
-1 - sqrt(3)/3 -3 - sqrt(3) ------------ = ----------- we can rationalize the 1 - sqrt(3)/3 3 - sqrt(3) denominator maybe :)
amistre64
  • 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
anonymous
  • anonymous
yes
amistre64
  • amistre64
yes im right? or yes if we agree theyll shut up? :)
anonymous
  • anonymous
um... both
amistre64
  • amistre64
lol .... i got enough voices in me head that we aint gonna shut up regardless lol
anonymous
  • anonymous
lol
amistre64
  • amistre64
sin(23/12) is this missing a pi?
anonymous
  • anonymous
ok so, the answer for the first one is -2sqrt3
amistre64
  • amistre64
no its: (-2) - (sqrt(3))
anonymous
  • anonymous
Yes, it is. It is sin(23pi/12)
amistre64
  • 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
anonymous
  • anonymous
ok
anonymous
  • anonymous
why r u rounding up to 24?
amistre64
  • amistre64
just looking at where the angle ends up; its tucked under the 2pi. 23pi/12 = 20pi/12 + 3pi/12
amistre64
  • amistre64
20pi/12 = 5pi/3 3pi/12 = pi/4
amistre64
  • amistre64
these are angles we know about, so we can use these
anonymous
  • anonymous
ok
amistre64
  • amistre64
sin(23pi/12) = sin(5pi/3 + pi/4) sin(a+b) = sin(a)cos(b)+sin(b)cos(a)
amistre64
  • amistre64
sin(5pi/3) = -sqrt(3)/2 cos(5pi/3) = 1/2 sin(pi/4) = cos(pi/4) = 1/sqrt(2)
anonymous
  • anonymous
is the answer [sqrt3-1]/ [2sqrt2]
amistre64
  • amistre64
sin(a+b) = (-sqrt(2)/2) (1/sqrt(2)) +(1/sqrt(2))(1/2)
amistre64
  • amistre64
-2/4 + sqrt(2)/4 = sqrt(2)-2 -------- 4
amistre64
  • amistre64
ack!!...i typoed that up didnt I
anonymous
  • anonymous
yes
amistre64
  • amistre64
(-sqrt(3)/2) (1/sqrt(2)) +(1/sqrt(2))(1/2) -sqrt(6)/4 + sqrt(2)/4 = sqrt(2) - sqrt(6) -------------- 4
amistre64
  • amistre64
that should be correct :)
anonymous
  • anonymous
let's see...
amistre64
  • amistre64
im going for coffee......like a bad little mormon :)
anonymous
  • anonymous
Correct!
anonymous
  • anonymous
haha...
anonymous
  • anonymous
have we done the third one?
amistre64
  • amistre64
theres a third one? and the watering hole is getting refilled .....
anonymous
  • anonymous
you* sorry for taking the credit :P
anonymous
  • anonymous
It is cos(13pi/12)
amistre64
  • amistre64
your like my conscinece....that is if I had a consicence lol
amistre64
  • amistre64
pi/12 = 15 degrees. I knew it!!
amistre64
  • amistre64
this is 225 - 30 degrees.... or 5pi/4 - pi/6
amistre64
  • amistre64
cos(a-b) - cos(a)cos(b) + sin(a)sin(b)
amistre64
  • amistre64
sin and cos 5pi/4 = -1/sqrt(2) (a) sin 30 = 1/2 cos30 = sqrt(3)/2
anonymous
  • anonymous
How the hell do you know all of this?
amistre64
  • amistre64
(-1/sqrt(2)) (sqrt3)/2) + (-1/sqrt(2)) (1/2) -sqrt(6)/4 + -sqrt(2)/4 = -sqrt(6) -sqrt(2) -------------- 4
amistre64
  • amistre64
I know nutheeeng!!
anonymous
  • anonymous
kidding me
amistre64
  • amistre64
col. klink right?
anonymous
  • anonymous
can u help me with more? PLEASEEEEEEE:)
amistre64
  • amistre64
was I right?
anonymous
  • anonymous
Oh yeah....
amistre64
  • 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;)
anonymous
  • anonymous
THANK YOU SO MUCH!!!
amistre64
  • amistre64
its all about the benjamins baybay lol
anonymous
  • anonymous
Use an addition or subtraction formula to find the exact value of the expression. Tan(-15degrees)
anonymous
  • anonymous
yep
amistre64
  • amistre64
sin juice is sitting on the table again; brb....
anonymous
  • anonymous
ok
amistre64
  • amistre64
the tan(-15) degrees = tan(-pi/12) = tan(23pi/12)
amistre64
  • amistre64
lets go with 45 - 30; cause 15 = pi/12
anonymous
  • 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 :'(
anonymous
  • anonymous
ok
amistre64
  • amistre64
im gonna guess that the tan(-15) = -sqrt(3)/6 but let me verify that with my sources ;)
anonymous
  • anonymous
you're your own source lol
anonymous
  • anonymous
it's wrong, my hw program says it's wrong
amistre64
  • amistre64
I aint verified it yet....hold on lol
amistre64
  • 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)
anonymous
  • anonymous
ok
amistre64
  • amistre64
1 -2sqrt(3)/3 + 3/9 ------------------ 1 - 3/9
amistre64
  • amistre64
9 -6sqrt(3) + 3 ----------- 9 ------------- 9-3 --- 9
amistre64
  • 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
anonymous
  • anonymous
Righto... :)
amistre64
  • amistre64
i read it in the stars lol
anonymous
  • 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 :'(
anonymous
  • anonymous
haha...
amistre64
  • 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
amistre64
  • amistre64
cos(120) = -1/2
anonymous
  • anonymous
how do you get cos120 = -1/2
amistre64
  • 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
anonymous
  • anonymous
oh ok...
amistre64
  • amistre64
weird als got a paradoy called "its all about the pentiums baby"! its hilarious
anonymous
  • anonymous
haha... lol. Is he still around?
anonymous
  • anonymous
This is hilarious http://www.youtube.com/watch?v=3u-J4uxEWFQ
amistre64
  • amistre64
the hit i put out on him hasnt been paid yet, so yeah :)
anonymous
  • anonymous
Damn it!
amistre64
  • amistre64
libraries conputers to old....says it needs a java update but wont take it :/
anonymous
  • anonymous
ah... what school or college do u go to?
amistre64
  • amistre64
phcc down here in florida
anonymous
  • anonymous
oh.. ok
anonymous
  • anonymous
i'm at umd- college park
amistre64
  • amistre64
maryland?
anonymous
  • anonymous
yeah
amistre64
  • amistre64
annapolis is your capital lol
anonymous
  • anonymous
good job :) A+
anonymous
  • anonymous
u should be at MIT or CAL-TECH lol
amistre64
  • amistre64
it took me 39 years to memorize the states and their capitals :) now its just useless junk rattling around...
anonymous
  • anonymous
yep...
anonymous
  • anonymous
my parents have been telling me that since i was born lol this stuff will get you somewhere not remembering capitals
anonymous
  • anonymous
but back to the problem...
amistre64
  • amistre64
which problem we got now?
anonymous
  • 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 :'(
amistre64
  • amistre64
dint we just finish that one?
amistre64
  • amistre64
cos(120) = -1/2
anonymous
  • anonymous
sorry we u did that one already
anonymous
  • anonymous
Simplify the trigonometric expression. cos(x)/sec(x) + sin(x)/csc(x)
amistre64
  • amistre64
its like im stuck in a time warp that leads thru the twilight zone .....
amistre64
  • amistre64
is that a left term + a right term? or is that right side all under the fraction bar? use them () to seperate things up
anonymous
  • anonymous
it is a left arm and a right arm
anonymous
  • anonymous
\[\cos [x]\div \sec [x] +\sin [x]\div \csc [x]\] If this helps
amistre64
  • amistre64
sec = 1/cos csc = 1/sin 1+1 = 2
amistre64
  • amistre64
next!!
anonymous
  • anonymous
Use an addition or subtraction formula to write the expression as a trigonometric function of one number, and then find its exact value. tan(pi/3) + tan(5pi/6) / 1- tan(pi/3) tan(5pi/6)
amistre64
  • amistre64
thats the expanded version of tan(a+b) a = pi/3 b = 5pi/6
anonymous
  • anonymous
ok
amistre64
  • amistre64
pi/3 + 5pi/6 = 2pi +... = 7pi/6 = pi + pi/6
amistre64
  • amistre64
tan(7pi/6) = tan(pi/6) = tan(30) = 1/sqrt(3) = sqrt(3)/3
anonymous
  • anonymous
1) Use an addition or subtraction formula to write the expression as a trigonometric function of one number, and then find its exact value. cos(10) cos(80) - sin(10) sin(80) 2) Use an addition or subtraction formula to find the exact value of the expression. sin(15)
amistre64
  • amistre64
1 is a cos(a+b) cos(10+80) = cos(90) = 0 2) sin(pi/12)..dint we do that one earlier?
anonymous
  • anonymous
no
amistre64
  • amistre64
it looks familiar :)
anonymous
  • anonymous
Use an addition or subtraction formula to find the exact value of the expression. sin(15)
amistre64
  • amistre64
we did the cos(13/12pi)...which is pretty much what we want with a sign adjustment
amistre64
  • amistre64
sqrt(6)+sqrt(2) cos(pi/12) = -------------- 4 cos^2 + sin^2 = 1 sqrt(6)+sqrt(2) 8+4sqrt(3) -------------- = ----------- 4 16 8+4sqrt(3) 1 - ----------- = sin^2(15) 16
amistre64
  • amistre64
8 -4sqrt(3) ------------- = sin^2(15) 16
amistre64
  • amistre64
4 (2 -sqrt(3)) sqrt ------------- = sin(15) 16
amistre64
  • amistre64
sqrt(2-sqrt(3)) ------------- = sin(15) maybe? 2
anonymous
  • anonymous
that doesn't work
amistre64
  • amistre64
\[\sqrt{2 - \sqrt{3}}/2\]
amistre64
  • amistre64
how you get a bar for a fraction in this thing?
anonymous
  • anonymous
u can't i tried doing it to
amistre64
  • amistre64
if anything; sin(45-30) = sin(15) sin(45-30) = sin(1/sqrt(2))cos(1/sqrt(3))-sin(1/2)cos(1/sqrt(2))
amistre64
  • amistre64
lol....right concept wrong format lol take out those sin cos stuff, its left over from my inner most deepest thoughts :)
amistre64
  • amistre64
(1/sqrt(2)) (1/sqrt(3)) - (1/2) (1/sqrt(2)) 1/sqrt(6) - 1/2sqrt(2)
amistre64
  • amistre64
sqrt(6)/6 - sqrt(2)/4 2sqrt(6)/12 - 3sqrt(2)/12 2sqrt(6) - 3sqrt(2) ---------------- ??? 12
amistre64
  • amistre64
not it... i see where I messed it up lol
amistre64
  • amistre64
(1/sqrt(2)) (sqrt(3)/2) - (1/2) (1/sqrt(2)) sqrt(6)/4 - sqrt(2)/4 sqrt(6) - sqrt(2) -------------- should be it 4
anonymous
  • anonymous
You are correct :)
anonymous
  • anonymous
Simplify the trigonometric expression. csc(x) - sin(x) / cot(x) Write the trigonometric expression in terms of sine and cosine, and then simplify. sin(t)sec(t)
anonymous
  • anonymous
U know I'm actually learning from u :)
amistre64
  • amistre64
clean that up for me....
amistre64
  • amistre64
csc(x) - sin(x) / cot(x) is not very clear...
anonymous
  • anonymous
Simplify the trigonometric expression. csc(x) - sin(x) over or divided by cot(x)
anonymous
  • anonymous
That helps?
amistre64
  • amistre64
csc(x) - sin(x) ------------ ??? cot(x)
anonymous
  • anonymous
yes

Looking for something else?

Not the answer you are looking for? Search for more explanations.