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sierraurb Group Title

Trignometric functions help!!

  • one month ago
  • one month ago

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  1. sierraurb Group Title
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    prove \[\sin \Theta -\sin \Theta \times \cos ^{2}\Theta =\sin ^{3}\Theta \] show all work

    • one month ago
  2. sierraurb Group Title
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    I get that you'd start by multiplying sin(theta) and cos^2(theta) but idk what that comes out to

    • one month ago
  3. cwrw238 Group Title
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    use a substitution by the identity cos^2 theta = 1 - sin^2 theta

    • one month ago
  4. sierraurb Group Title
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    I have no idea what that means :( this is the one question i have no clue how to do

    • one month ago
  5. cwrw238 Group Title
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    instead of cos^ theta write 1 - sin^ theta then simplify and you'll find you'll get sin^3 theta

    • one month ago
  6. sierraurb Group Title
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    But its cos^2theta

    • one month ago
  7. cwrw238 Group Title
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    cos^2 theta = 1 - sin^2 theta is an established trig identity

    • one month ago
  8. sierraurb Group Title
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    Okay so how would i use that identity to solve?

    • one month ago
  9. sierraurb Group Title
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    should i replace cos^2 theta with 1-sin^2

    • one month ago
  10. cwrw238 Group Title
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    sin theta - sin theta * cos^ theta = sin theta - sin theta ( 1 - sin^2 theta) now expand the brackets and simplify

    • one month ago
  11. cwrw238 Group Title
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    yes i've replaced cos^2 theta with 1 - sin^2 theta

    • one month ago
  12. sierraurb Group Title
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    do i subctract the two sin theta's or distribute the one?

    • one month ago
  13. cwrw238 Group Title
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    distribute the sin theta over the parentheses is the next step

    • one month ago
  14. cwrw238 Group Title
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    * rather you distribute - sin theta

    • one month ago
  15. sierraurb Group Title
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    so its sin theta - sin theta - sin^3 theta

    • one month ago
  16. sierraurb Group Title
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    and the two sin theta's cancel out and leave me with sin^3 theta?

    • one month ago
  17. cwrw238 Group Title
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    no - remember:- - times - = +

    • one month ago
  18. cwrw238 Group Title
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    yes ( but note the sign of sin^3 theta is positive)

    • one month ago
  19. sierraurb Group Title
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    I understand now!! Thank you so so much I appreciate it a lot :)

    • one month ago
  20. cwrw238 Group Title
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    - sin theta - sin^2 theta = + sin^3 theta

    • one month ago
  21. cwrw238 Group Title
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    yw

    • one month ago
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