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Sona
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how wud u solve the following?
\[\cos (\tan^{1} (5/12)+\tan^{1} (15/8))\]
Plz help this is in 15 min!
 2 years ago
 2 years ago
Sona Group Title
how wud u solve the following? \[\cos (\tan^{1} (5/12)+\tan^{1} (15/8))\] Plz help this is in 15 min!
 2 years ago
 2 years ago

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cnknd Group TitleBest ResponseYou've already chosen the best response.0
ok do the numbers (5,12, ) and (8,15, ) remind you of something?
 2 years ago

cnknd Group TitleBest ResponseYou've already chosen the best response.0
these numbers appear in the problem for good reason
 2 years ago

Sona Group TitleBest ResponseYou've already chosen the best response.0
umm im not sure way u mean
 2 years ago

cnknd Group TitleBest ResponseYou've already chosen the best response.0
ok let me fill in the blanks: (5,12,13), (8,15,17). do these numbers look familiar?
 2 years ago

Sona Group TitleBest ResponseYou've already chosen the best response.0
these r (x y r) values?
 2 years ago

cnknd Group TitleBest ResponseYou've already chosen the best response.0
pythagorean triples. i.e. integer side lengths for right triangles
 2 years ago

Sona Group TitleBest ResponseYou've already chosen the best response.0
ok then wat do i do w/this #?
 2 years ago

Sona Group TitleBest ResponseYou've already chosen the best response.0
don't mean to rush but this is due online in 10 min exactly
 2 years ago

cnknd Group TitleBest ResponseYou've already chosen the best response.0
so you know [\tan^{1} (5/12)] refers to the 5,12,13 triangle, and [\tan^{1} (15/8)] refers to the 8,15,17 triangle
 2 years ago

cnknd Group TitleBest ResponseYou've already chosen the best response.0
ugh sry not familiar with the mathtype syntax here... i apologize for poorly formatted equations
 2 years ago

Sona Group TitleBest ResponseYou've already chosen the best response.0
its ok don't worry bout its understandable
 2 years ago

cnknd Group TitleBest ResponseYou've already chosen the best response.0
now the 2 inverse tangents give you to angles. let's call them a and b. the angle a comes from the 5,12,13 triangle, and the angle b comes from the 8,15,17 triangle
 2 years ago

cnknd Group TitleBest ResponseYou've already chosen the best response.0
draw your triangles, and identify which angle is a, and which angles is b
 2 years ago

cnknd Group TitleBest ResponseYou've already chosen the best response.0
now back at the original equation, since i'm lazy and don't want to write out all the inverse tangents, i'll just write a and b: cos(a+b) = cos(a) cos(b)  sin(a) sin(b)
 2 years ago

cnknd Group TitleBest ResponseYou've already chosen the best response.0
from your triangles, you should be able to identify what cos(a), cos(b), sin(a), and sin(b) are
 2 years ago

Sona Group TitleBest ResponseYou've already chosen the best response.0
so y for the 1st one is 5 n x is 12 while the 2nd y is 15 n 2nd x is 8?
 2 years ago

cnknd Group TitleBest ResponseYou've already chosen the best response.0
dw:1353483877024:dw
 2 years ago

cnknd Group TitleBest ResponseYou've already chosen the best response.0
sry, diagram not drawn to scale
 2 years ago

Sona Group TitleBest ResponseYou've already chosen the best response.0
thats fine but I'm still stuck :(
 2 years ago

cnknd Group TitleBest ResponseYou've already chosen the best response.0
ok back to original equation remember a = tan1(5/12) and b = tan1(15/8) so the original equation: cos(a+b), can be expanded as cos(a)cos(b)  sin(a)sin(b)
 2 years ago

cnknd Group TitleBest ResponseYou've already chosen the best response.0
now look at the pictures, what's cos(a)? what's cos(b)? what's sin(a)? what's sin(b)? (remember cos is adjacent/hypotenuse, sin is opposite/hypotenuse)
 2 years ago

akinfermo Group TitleBest ResponseYou've already chosen the best response.0
you should make a change of variables
 2 years ago
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