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LaddiusMaximus

  • 5 years ago

cosx/1-sinx -1/cosx = tanx what happens to the 1-sinx? I know 1/cosx becomes sec, but what then?

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  1. amistre64
    • 5 years ago
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    it should "post" when you hit "post" .....

  2. anonymous
    • 5 years ago
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    flip the order and you will have : -1-sinx/cosx = -1/cosx -sinx/cosx sinx/cosx = tanx so; -1/cosx - tanx = -secx-tanx

  3. anonymous
    • 5 years ago
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    I guess

  4. amistre64
    • 5 years ago
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    cos - 1 sin ----- --- = --- is this the equation? 1-sin cos cos

  5. LaddiusMaximus
    • 5 years ago
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    yes

  6. LaddiusMaximus
    • 5 years ago
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    would algebra be the first step? common denominators?

  7. amistre64
    • 5 years ago
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    give it a shot :)

  8. LaddiusMaximus
    • 5 years ago
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    I thought at first using the reciprocal identity for the 1/cos

  9. LaddiusMaximus
    • 5 years ago
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    okay now I have sin^2x/1-sinxcosx

  10. LaddiusMaximus
    • 5 years ago
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    which then becomes sinx/1-cosx

  11. amistre64
    • 5 years ago
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    thinking......(12% loaded)

  12. amistre64
    • 5 years ago
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    thinking done... got it :)

  13. amistre64
    • 5 years ago
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    get like denoms is good; multiply cos/(1-sin) by (cos/cos) to get what?

  14. amistre64
    • 5 years ago
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    and 1/cos get multiplied by (1-sin)/(1-sin) to get??

  15. amistre64
    • 5 years ago
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    cos^2 - (1-sin) ------------ right? cos(1-sin)

  16. amistre64
    • 5 years ago
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    work the top out to: cos^2 + sin -1 ; cos^2 = 1-sin^2 1-sin^2 + sin - 1 ; 1-1 = 0 sin - sin^2 ; factor out a "sin" sin(1-sin) is the top; cancel out (1-sin) top to bottom to get: sin/cos = tan....TADA!!!

  17. amistre64
    • 5 years ago
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    you follow that alright?

  18. LaddiusMaximus
    • 5 years ago
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    yeah but I ended up with cos^2x-1/1-sinxcosx

  19. LaddiusMaximus
    • 5 years ago
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    then sin^2x/1-sinxcosx

  20. amistre64
    • 5 years ago
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    the bottom aint 1-sincos; its cos(1-sin)

  21. amistre64
    • 5 years ago
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    cos cos - (1-sin) -------- ------- right?? cos(1-sin) cos(1-sin)

  22. amistre64
    • 5 years ago
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    to get like denoms; you need to multiply each side by a convenient form of (1)

  23. amistre64
    • 5 years ago
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    cos/cos = 1 AND (1-sin)/(1-sin) = 1

  24. LaddiusMaximus
    • 5 years ago
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    ohhhh duh

  25. amistre64
    • 5 years ago
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    lol ..... mathmatikers are tricky like that :)

  26. LaddiusMaximus
    • 5 years ago
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    then I start canceling out like numbers right?

  27. amistre64
    • 5 years ago
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    there some manipulations first.

  28. amistre64
    • 5 years ago
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    the bottom is good; so play with the top.

  29. LaddiusMaximus
    • 5 years ago
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    so cosx cosx - (1-sinx) becomes cos^2x -(1-sinx)

  30. amistre64
    • 5 years ago
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    good; now what multiply out the -(1-sin). what do we get?

  31. LaddiusMaximus
    • 5 years ago
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    1+sinx

  32. amistre64
    • 5 years ago
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    good; and how can we play with cos^2 to make it in terms of "sin"? what does cos^2 =?

  33. LaddiusMaximus
    • 5 years ago
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    sin^2x

  34. LaddiusMaximus
    • 5 years ago
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    pythagorean identity?

  35. amistre64
    • 5 years ago
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    close.... yes, pyth identity. sin^2 + cos^2 = 1 solve for cos^2, what do we get? subtract sin^2 from each side: cos^2 = 1-sin^2

  36. amistre64
    • 5 years ago
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    our top becomes what with this information?

  37. LaddiusMaximus
    • 5 years ago
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    1-sin^2x-1+sinx

  38. amistre64
    • 5 years ago
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    not ..... -1+sin. remember we already took care of that part. It was equal to: +1+sin do you see that? do you understand how we did it?

  39. LaddiusMaximus
    • 5 years ago
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    but I thought -(1-sinx) would become -1+sinx - times one is -1 and - times -sinx would become +sinx

  40. anonymous
    • 5 years ago
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    lol. now I'm lost ._.

  41. amistre64
    • 5 years ago
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    you know what.... YOU are correct. I was wrong.... carry on please :)

  42. anonymous
    • 5 years ago
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    who?

  43. amistre64
    • 5 years ago
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    Laddi was right. And im glad Laddi caught it; have confidence in yourself :)

  44. anonymous
    • 5 years ago
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    sorry for the wrong answer laddi!

  45. amistre64
    • 5 years ago
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    1-sin^2-1+sin what can we do with this?

  46. anonymous
    • 5 years ago
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    replace 1-sin^2 with cose^2

  47. amistre64
    • 5 years ago
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    sst; only if we wanna work backwards... lets try to work forwards :)

  48. anonymous
    • 5 years ago
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    but why?

  49. LaddiusMaximus
    • 5 years ago
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    does it become sinx?

  50. amistre64
    • 5 years ago
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    lets rewrite it this way: 1-1+sin-sin^2 now what do we do?

  51. LaddiusMaximus
    • 5 years ago
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    well 1-1 becomes 0, so sin-sin^2 is left.

  52. amistre64
    • 5 years ago
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    very good; how can we work this? can we factor anything out to make it look more like the bottom of the fraction? remember the bottom looks like this: cos(1-sin)

  53. amistre64
    • 5 years ago
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    think of the top as: x-x^2 if it helps

  54. LaddiusMaximus
    • 5 years ago
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    sinx can factor out 1-sinx

  55. anonymous
    • 5 years ago
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    why don't you just flip cos/1-sin so it will be -(1-sin)/cos?

  56. amistre64
    • 5 years ago
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    very good :) that leaves us with: sin(1-sin) sin -------- = --- cos(1-sin) cos can you see that we can do now?

  57. amistre64
    • 5 years ago
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    sst; because you change its value if you do that and make a different equation. does 2/x = x/2 for all "x"?

  58. anonymous
    • 5 years ago
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    no ofcourse not it's equal to -x/2 ^^

  59. anonymous
    • 5 years ago
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    wait, I get what you mean now ^^"

  60. LaddiusMaximus
    • 5 years ago
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    wait a minute how did (1-sin) get up top? I had sinx+sin^2x

  61. amistre64
    • 5 years ago
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    lol .... at least one of us does :)

  62. anonymous
    • 5 years ago
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    see, you flipped it!

  63. anonymous
    • 5 years ago
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    I knew it

  64. amistre64
    • 5 years ago
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    we had: 1-1+sin-sin^2 = sin-sin^2 = sin(1-sin)

  65. myininaya
    • 5 years ago
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    find common denominator which you guys did! Good! [ (cosx)^2-1]/[(1-sin(x))(cosx)]

  66. myininaya
    • 5 years ago
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    Now 1=(cosx)^2+(sinx)^2

  67. myininaya
    • 5 years ago
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    Replace 1 with that

  68. myininaya
    • 5 years ago
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    The (cosx)^2 cancel out

  69. anonymous
    • 5 years ago
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    there's still more? I thought the question was answered

  70. myininaya
    • 5 years ago
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    The nemerator has -(sinx)^2+sinx

  71. LaddiusMaximus
    • 5 years ago
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    ok confusion. 1-sin^2x-1+sinx becomes what?

  72. amistre64
    • 5 years ago
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    myin; your equation is skewed look at what you posted again :)

  73. myininaya
    • 5 years ago
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    You can factor out a (sinx) leaving with sinx(-sinx+1)

  74. LaddiusMaximus
    • 5 years ago
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    sin^2x+sinx

  75. amistre64
    • 5 years ago
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    Laddi: (-sin^2) + sin dont forget you (-)

  76. myininaya
    • 5 years ago
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    You can do a cancellation leaving you with the desired reult

  77. amistre64
    • 5 years ago
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    1 (-)sin^2 (-)1 (+)sin becomes: (-)sin^2 (+)sin

  78. LaddiusMaximus
    • 5 years ago
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    okay, then what?

  79. myininaya
    • 5 years ago
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    Factor out what they have in common which is a sinx

  80. amistre64
    • 5 years ago
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    then we factor out a (+sin) to get: sin(1-sin) correct?

  81. LaddiusMaximus
    • 5 years ago
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    okay so -sinx is left on top?

  82. myininaya
    • 5 years ago
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    The numerator gives you sinx(-sinx+1)

  83. anonymous
    • 5 years ago
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    no sinx(sinx - 1)

  84. LaddiusMaximus
    • 5 years ago
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    wait a minute. okay right now I have -sin^2x +sinx/cosx(1-sinx)

  85. myininaya
    • 5 years ago
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    No ss the sinx is negative and the 1 is postive

  86. amistre64
    • 5 years ago
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    good Laddi;

  87. LaddiusMaximus
    • 5 years ago
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    so -sin^2x factors out the +sinx?

  88. amistre64
    • 5 years ago
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    yes...

  89. LaddiusMaximus
    • 5 years ago
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    so im left with -sinx/cosx(1-sinx)

  90. myininaya
    • 5 years ago
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    You should be left with [(sinx(-sinx+1)]/[cosx(1-sinx)]

  91. myininaya
    • 5 years ago
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    Does anything cancel?

  92. amistre64
    • 5 years ago
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    (-sin^2 +sin)/cos(1-sin) becomes... sin(1-sin) / cos(1-sin)

  93. anonymous
    • 5 years ago
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    I'll just wacth ^-^

  94. myininaya
    • 5 years ago
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    -sinx+1=1-sinx So that part in you numerator cancels out with that part in the denominator

  95. amistre64
    • 5 years ago
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    Laddi: Does -sin^2 + sin = sin(1-sin) ???

  96. anonymous
    • 5 years ago
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    -sin(sin -1)

  97. LaddiusMaximus
    • 5 years ago
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    I didnt think it did.

  98. anonymous
    • 5 years ago
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    or sin(-sin + 1) = sin (1-sin)

  99. anonymous
    • 5 years ago
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    ^^

  100. anonymous
    • 5 years ago
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    lol, yes u were right

  101. LaddiusMaximus
    • 5 years ago
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    now im confused.

  102. amistre64
    • 5 years ago
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    this "find the moving textbox" is rather annoying. They need to find a way to simply "post" your responses without having to play "TAG"

  103. amistre64
    • 5 years ago
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    Laddi: lets figure this part out: -sin^2 + sin: can we rewrite this as: sin - sin^2?

  104. anonymous
    • 5 years ago
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    don't be confused, now laddi what do you have: -sin^2 + sin right? now take -sin outside, u'll be left with = -sin(sin-1) or you can take sin only outside and u'll be left with sin(-sin + 1) = sin(1-sin) apply the distributive property and you'll get it :)

  105. anonymous
    • 5 years ago
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    get it? ^^

  106. amistre64
    • 5 years ago
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    sst: one step at a time :)

  107. anonymous
    • 5 years ago
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    sorry ^^"

  108. LaddiusMaximus
    • 5 years ago
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    okay I got that part.

  109. anonymous
    • 5 years ago
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    awesome! amistre continue :)

  110. LaddiusMaximus
    • 5 years ago
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    okay then it becomes 1-sinx?

  111. LaddiusMaximus
    • 5 years ago
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    that sinx doesnt go away. one takes it place when it factors a sinx out of sin^2x

  112. amistre64
    • 5 years ago
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    Laddi; yes

  113. LaddiusMaximus
    • 5 years ago
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    so sin-sin^2x becomes 1-sinx

  114. amistre64
    • 5 years ago
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    it becomes.... pull a sin out...... sin(1-sin) right?

  115. myininaya
    • 5 years ago
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    Trig identities are the BEST!

  116. LaddiusMaximus
    • 5 years ago
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    wait what?

  117. LaddiusMaximus
    • 5 years ago
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    i thought sinx-sin^2x becomes 1-sinx?

  118. anonymous
    • 5 years ago
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    laddi, 4 = 2 x 2 right? let's say we have 4 - 2x, factor what will the answer be?

  119. myininaya
    • 5 years ago
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    it becomes sinx(1-sinx)

  120. anonymous
    • 5 years ago
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    2(2-x) right?

  121. amistre64
    • 5 years ago
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    sin - sin^2. pull out a "sin" put it to the outside... sin (1 - sin) if we multiply it back in we get: sin(1) - sin(sin) = sin - sin^2

  122. anonymous
    • 5 years ago
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    imagine the 2 as sinx :)

  123. anonymous
    • 5 years ago
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    so instead of 4- 2x we have = 2(2-x) sin^2 - sin = sin(1-sin) ta da!

  124. anonymous
    • 5 years ago
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    same story ^^

  125. amistre64
    • 5 years ago
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    it is basic algebra... thats all

  126. LaddiusMaximus
    • 5 years ago
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    havent taken basic algebra in over 10yrs

  127. anonymous
    • 5 years ago
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    or or or, sin^2 = sin x sin right? pull one sin outside as a common factor , we're left with sin(1-sin) :)

  128. anonymous
    • 5 years ago
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    did u get my example? :)

  129. amistre64
    • 5 years ago
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    lol .... it was 20 years for me when I went back to college..

  130. anonymous
    • 5 years ago
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    laddi did you understand my example? with the 2 thingy?

  131. LaddiusMaximus
    • 5 years ago
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    yeah its hard to conceptualize right now.

  132. myininaya
    • 5 years ago
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    oh wow i like that word. is that a word conceptualize?

  133. amistre64
    • 5 years ago
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    try to recall this: 5a- a^2 = a(5-a)

  134. LaddiusMaximus
    • 5 years ago
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    hmm I get it now that Im looking at it on paper. sheesh

  135. anonymous
    • 5 years ago
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    (sin)(sin) - sin we are going to steal one sin! then...we're left with one sin, soooo, sin(1-sin) to check multiply the (1-sin) with sin , it's going to be equal to ! sin^2-sin! AWESOME!

  136. anonymous
    • 5 years ago
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    ^_^

  137. amistre64
    • 5 years ago
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    paper helps too :)

  138. anonymous
    • 5 years ago
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    and a marker

  139. anonymous
    • 5 years ago
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    and some juice

  140. anonymous
    • 5 years ago
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    and a nap too

  141. anonymous
    • 5 years ago
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    good luck laddi hope u got it now :)

  142. amistre64
    • 5 years ago
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    nap would be nice :)

  143. myininaya
    • 5 years ago
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    More Math!

  144. LaddiusMaximus
    • 5 years ago
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    so when you take a sin away it becomes 1?

  145. myininaya
    • 5 years ago
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    You aren't really taking it away. That 1 is being multiplied by that sinx

  146. LaddiusMaximus
    • 5 years ago
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    so its more of a standard? 5(a-a^2) becomes 5a-5a^2?

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spraguer (Moderator)
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