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Sona

  • 2 years ago

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

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  1. cnknd
    • 2 years ago
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    ok do the numbers (5,12, ) and (8,15, ) remind you of something?

  2. cnknd
    • 2 years ago
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    these numbers appear in the problem for good reason

  3. Sona
    • 2 years ago
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    umm im not sure way u mean

  4. cnknd
    • 2 years ago
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    ok let me fill in the blanks: (5,12,13), (8,15,17). do these numbers look familiar?

  5. Sona
    • 2 years ago
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    these r (x y r) values?

  6. cnknd
    • 2 years ago
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    pythagorean triples. i.e. integer side lengths for right triangles

  7. Sona
    • 2 years ago
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    ok then wat do i do w/this #?

  8. Sona
    • 2 years ago
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    don't mean to rush but this is due online in 10 min exactly

  9. cnknd
    • 2 years ago
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    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

  10. cnknd
    • 2 years ago
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    ugh sry not familiar with the mathtype syntax here... i apologize for poorly formatted equations

  11. Sona
    • 2 years ago
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    its ok don't worry bout its understandable

  12. cnknd
    • 2 years ago
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    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

  13. cnknd
    • 2 years ago
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    draw your triangles, and identify which angle is a, and which angles is b

  14. cnknd
    • 2 years ago
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    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)

  15. cnknd
    • 2 years ago
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    from your triangles, you should be able to identify what cos(a), cos(b), sin(a), and sin(b) are

  16. Sona
    • 2 years ago
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    so y for the 1st one is 5 n x is 12 while the 2nd y is 15 n 2nd x is 8?

  17. cnknd
    • 2 years ago
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    |dw:1353483877024:dw|

  18. cnknd
    • 2 years ago
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    sry, diagram not drawn to scale

  19. Sona
    • 2 years ago
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    thats fine but I'm still stuck :(

  20. cnknd
    • 2 years ago
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    ok back to original equation remember a = tan-1(5/12) and b = tan-1(15/8) so the original equation: cos(a+b), can be expanded as cos(a)cos(b) - sin(a)sin(b)

  21. cnknd
    • 2 years ago
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    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)

  22. akinfermo
    • 2 years ago
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    you should make a change of variables

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