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anonymous

  • one year ago

If cosine of x equals 1 over 2, what is sin(x) and tan(x)? Explain your steps in complete sentences.

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  1. freckles
    • one year ago
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    make a right triangle then use cos(x)=1/2 then use Pythagorean theorem to figure out opposite side of x

  2. freckles
    • one year ago
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    then you have everything you need to find sin(x) and tan(x)

  3. anonymous
    • one year ago
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    can u guide me @freckles

  4. freckles
    • one year ago
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    which part do you need help on?

  5. freckles
    • one year ago
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    did you draw the right triangle yet?

  6. anonymous
    • one year ago
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    i guess all.

  7. anonymous
    • one year ago
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    yes

  8. freckles
    • one year ago
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    ok then use cos(x)=1/2 remember cosine, think adjacent/hyp

  9. anonymous
    • one year ago
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    ok

  10. freckles
    • one year ago
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    then use the Pythagorean theorem to find the opp side can you do that?

  11. anonymous
    • one year ago
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    no

  12. freckles
    • one year ago
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    well we know the Pythagorean theorem says: \[opp^2+adj^2=hyp^2 \\ \text{ and we know the } adj \text{ and the hyp } \\ \text{ just solve for opp}\]

  13. anonymous
    • one year ago
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    adj is 1 and hyp is 2?

  14. freckles
    • one year ago
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    yes this was given by cos(x)=1/2 you could also use any thing that reduces down to 1/2 for example cos(x)=10/20 and call the adj=10 and hyp=20 but it doesn't matter in the end we will get the same reduced fractions so yes you can use adj=1 and hyp=2

  15. anonymous
    • one year ago
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    ok

  16. freckles
    • one year ago
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    have you solved for opp yet?

  17. freckles
    • one year ago
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    if you have you can find sin(x) and tan(x)

  18. anonymous
    • one year ago
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    still working on it

  19. anonymous
    • one year ago
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    opp is root 5?

  20. freckles
    • one year ago
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    \[oop^2+1^2=2^2 \\ oop^2+1=4\] 4-1 isn't 5 should be 3

  21. freckles
    • one year ago
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    \[opp^2=4-1 \\ opp^2=3 \\ opp= \pm \sqrt{3}\]

  22. anonymous
    • one year ago
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    shoot my bad

  23. freckles
    • one year ago
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    so you have two answers for both sin(x) and tan(x) because of the plus or minus thing

  24. freckles
    • one year ago
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    anyways recall sin(x)=opp/hyp and tan(x)=opp/adj

  25. anonymous
    • one year ago
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    ok

  26. anonymous
    • one year ago
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    sin(x) = 3/2 tan(x) = 3/1 = 3

  27. anonymous
    • one year ago
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    @freckles

  28. freckles
    • one year ago
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    what happen to the sqrt( ) part ?

  29. freckles
    • one year ago
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    also you should have two answers for each

  30. freckles
    • one year ago
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    \[\sin(x)=\frac{ \pm \sqrt{3}}{2} \text{ this is the two answers for } \sin(x) \] now you try tan(x)=?

  31. anonymous
    • one year ago
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    ok

  32. anonymous
    • one year ago
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    ±root 3?

  33. freckles
    • one year ago
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    yep sounds great

  34. anonymous
    • one year ago
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    how did you get the root sighn tho

  35. anonymous
    • one year ago
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    sign

  36. anonymous
    • one year ago
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    jk never mind

  37. freckles
    • one year ago
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    \[opp^2+adj^2=hyp^2 \\ opp^2+1^2=2^2 \\ opp^2=4-1 \\ opp^2=3 \\ \text{ \to solve an equation like this you take square root of both sides }\]

  38. freckles
    • one year ago
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    but it will also mean you wind up with two possibilities since sqrt(opp^2)=|opp|=opp if opp>0 but =-opp if opp<0

  39. anonymous
    • one year ago
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    ok. Thank You so so so so much!!!!!!!!!!!!!!!!!!!

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