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sierraurb

  • one year ago

Trignometric functions help!!

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  1. sierraurb
    • one year ago
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    prove \[\sin \Theta -\sin \Theta \times \cos ^{2}\Theta =\sin ^{3}\Theta \] show all work

  2. sierraurb
    • one year ago
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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

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

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

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

  6. sierraurb
    • one year ago
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    But its cos^2theta

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

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

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

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

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

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

  13. cwrw238
    • one year ago
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    distribute the sin theta over the parentheses is the next step

  14. cwrw238
    • one year ago
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    * rather you distribute - sin theta

  15. sierraurb
    • one year ago
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    so its sin theta - sin theta - sin^3 theta

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

  17. cwrw238
    • one year ago
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    no - remember:- - times - = +

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

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

  20. cwrw238
    • one year ago
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    - sin theta - sin^2 theta = + sin^3 theta

  21. cwrw238
    • one year ago
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    yw

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