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anonymous

  • one year ago

ALGEBRA 2/TRIG HELP PLEASE PLEASE HELP

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  1. anonymous
    • one year ago
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    The point (2, 3) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.

  2. anonymous
    • one year ago
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    @ganeshie8 @pooja195

  3. anonymous
    • one year ago
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    @Chumpian

  4. anonymous
    • one year ago
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    @LynFran

  5. anonymous
    • one year ago
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    @Calcmathlete

  6. anonymous
    • one year ago
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    |dw:1437061318167:dw|Ok, first thing you need to do is find what the hypotenuse is. It's a right triangle, so can use the Pythagorean Theorem to figure out what the (?) on the drawing is?

  7. anonymous
    • one year ago
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    Is it 13?

  8. anonymous
    • one year ago
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    Close! The hypotenuse is \(\sqrt{13}\) since the hypotenuse squared is 13.|dw:1437061696572:dw|

  9. anonymous
    • one year ago
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    Okay :) what do I need to do next?

  10. anonymous
    • one year ago
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    So, now, we need to remember what sine, cosine, and tangent represent on a right triangle. The mnemonic device is SOH CAH TOA. S=Sine C=Cosine T=Tangent O=Opposite A=Adjacent H=Hypotenuse So, for example: \[\sin(\theta)=\frac{\text{side opposite of }\theta}{\text{hypotenuse}}\]The other 2, cosine and tangent work the same way in the mnemonic device. So, can you tell me what sine would be using this triangle?

  11. anonymous
    • one year ago
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    Sine would be 3/13, right? Which would make it 0.23076923076

  12. anonymous
    • one year ago
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    Wait, I forgot to square 13

  13. anonymous
    • one year ago
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    Remember, the hypotenuse is \(\sqrt{13}\), so \(\sin(\theta)=\frac{3}{\sqrt{13}}\)

  14. anonymous
    • one year ago
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    would it be 0.83205029433

  15. anonymous
    • one year ago
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    Nice. Using the mnemonic SOH CAH TOA, you can figure out what cosine and tangent represent. \[\cos(\theta)=\frac{\text{side adjacent to }\theta}{\text{hypotenuse}}\]\[\tan(\theta)=\frac{\text{side opposite to }\theta}{\text{side adjacent to }\theta}\]Can you figure out the rest?

  16. anonymous
    • one year ago
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    Cosine would be 2/√13=0.55470019622 and tangent would be 3/2=1.5

  17. anonymous
    • one year ago
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    Good job. I'd recommend for future reference, I'd just get it into your head that sine, cosine, and tangent are those ratios right there. It'll make your life easier as you go further into trig.

  18. anonymous
    • one year ago
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    Thank you so much!! :) You were a great help.

  19. anonymous
    • one year ago
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    Also, it didn't happen in this question, but remember, negatives stick with the calculation! So, if the point were in quadrant II (so the point would be (-2, 3)), then the x-value would be -2!! So, if you were given that, \(\sin(\theta)=\frac{3}{\sqrt{13}}\), \(\cos(\theta)=-\frac{2}{\sqrt{13}}\), and \(\tan(\theta)=-\frac{3}{2}\). See how the negative carried over?

  20. anonymous
    • one year ago
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    Oh, I see

  21. anonymous
    • one year ago
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    That's a good tip to remember; I almost always forget to carry the negative sign

  22. anonymous
    • one year ago
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    Thanks again :)

  23. anonymous
    • one year ago
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    np :)

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