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anonymous

  • one year ago

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

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  1. anonymous
    • one year ago
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    \[sinx = \frac{ 1 }{ 2 }\] as such correct?

  2. anonymous
    • one year ago
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    @iambatman yes

  3. anonymous
    • one year ago
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    Notice the ratio for sinx is \[\sin(x) = \frac{ \text{opposite} }{ \text{hypotenuse} }\] so we can make a right triangle |dw:1440123129207:dw| we can use pythagorean theorem to find the adjacent side, can you do that please?

  4. anonymous
    • one year ago
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    |dw:1440123246771:dw|

  5. anonymous
    • one year ago
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    @iambatman

  6. anonymous
    • one year ago
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    \[a^2+b^2 = c^2 \implies 1^2+b^2=2^2\]\[b^2 = 2^2 - 1^2 \implies b = \sqrt{4-1} = \sqrt{3}\] yup perfect!

  7. anonymous
    • one year ago
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    Now since we have adjacent side we should be able to find tanx and cosx now :)\[cosx = \frac{ \text{adjacent} }{ \text{hypotenuse} }\] \[tanx = \frac{ \text{opposite} }{ \text{adjcanet} }\]

  8. anonymous
    • one year ago
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    So far so good?

  9. anonymous
    • one year ago
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    yep! cos=rad3/2?

  10. anonymous
    • one year ago
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    Exactly! And tanx will be? :)

  11. anonymous
    • one year ago
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    and tan=1/rad3

  12. anonymous
    • one year ago
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    Perfect :) So we have \[\cos(x) = \frac{ \sqrt{3} }{ 2 }\] and \[\tan(x) = \frac{ 1 }{ \sqrt{3} }\] as you mentioned!

  13. anonymous
    • one year ago
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    so thats the whole answer

  14. anonymous
    • one year ago
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    Yup, that's it! Nice work

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