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anonymous

  • one year ago

If sine of x equals square root of 2 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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    @jamesr @Xaze @MoonMoonWolf @miszzkeriee @mathway @Michele_Laino @mickey1513

  2. anonymous
    • one year ago
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    Ok, we have \( \huge \sin x = \frac{\sqrt{2}}{2}\) So we know that \( \huge \sin \theta = \frac{y}{r}\) \( \huge y = \sqrt{2}\) r = radius \( \huge r = 2\) \( \huge \cos x = \frac{x}{r} \) Since we already know what y equals and r, we can use the following formula to find x \( \huge x^2 + y^2 = r^2 \) \( \huge x^2 + \sqrt{2}^2 = 2^2 \) \( \huge x^2 + \sqrt{2}^2 = 2^2 - \sqrt{2}^2 \) \( \huge \sqrt{x^2} = \sqrt{2^2 - \sqrt{2}^2} \) Can you finish solving for x ?

  3. anonymous
    • one year ago
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    Note, we are working on cos right now. We will do tan after cos.

  4. anonymous
    • one year ago
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    I tried but couldn't get it.

  5. anonymous
    • one year ago
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    @Nixy

  6. anonymous
    • one year ago
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    Ok, what did you get for x?

  7. anonymous
    • one year ago
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    4

  8. anonymous
    • one year ago
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    Ok, one sec

  9. anonymous
    • one year ago
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    By the way, using complete sentences how would I explain the key features of the graph of the tangent function?

  10. anonymous
    • one year ago
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    \( \huge \sqrt{x^2} = \sqrt{2^2 - \sqrt{2}^2} \) \( \huge \sqrt{x^2} = x\) \( \huge x = \sqrt{2^2 - \sqrt{2}^2} \) \( \huge 2^2 = 4 \) \( \huge \sqrt{2}^2 = \sqrt{4} = 2 \) So now we have \( \huge x = \sqrt{4 - 2} \) What is the value of x ?

  11. anonymous
    • one year ago
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    x = pie2

  12. anonymous
    • one year ago
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    Once you know how to solve the problem you should be able to explain.

  13. anonymous
    • one year ago
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    \( \huge x = \sqrt{2} \)

  14. anonymous
    • one year ago
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    Yeah

  15. anonymous
    • one year ago
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    So, \( \huge \cos x = \frac{x}{r}\) since we know what x is and r, we have cos x = \( \huge \frac{\sqrt{2}}{2} \)

  16. anonymous
    • one year ago
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    Since we have found cos, what do you think tan x =? \( \huge \tan x = \frac{y}{x} \)

  17. anonymous
    • one year ago
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    tan x would be pie2/4?

  18. anonymous
    • one year ago
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    Tan x = \( \huge \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} \) but you need to divide this

  19. anonymous
    • one year ago
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    Can you divide that?

  20. anonymous
    • one year ago
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    Wouldn't it equal 1?

  21. anonymous
    • one year ago
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    You are correct!!!!

  22. anonymous
    • one year ago
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    tan x = 1

  23. anonymous
    • one year ago
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    AYYYY

  24. anonymous
    • one year ago
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    so for the final answer how would i explain

  25. anonymous
    • one year ago
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    Just go over the steps that we went through here

  26. anonymous
    • one year ago
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    ok

  27. anonymous
    • one year ago
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    thank u

  28. anonymous
    • one year ago
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    YW

  29. anonymous
    • one year ago
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    but for this how would i explain

  30. anonymous
    • one year ago
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    Using complete sentences, explain the key features of the graph of the tangent function.

  31. anonymous
    • one year ago
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    Is that a separate question on your homework?

  32. anonymous
    • one year ago
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    nah separate

  33. anonymous
    • one year ago
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    It is separate ?

  34. anonymous
    • one year ago
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    yes

  35. anonymous
    • one year ago
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    Ok, you just need to explain the key feature of the tan when it comes to graphing.

  36. anonymous
    • one year ago
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    Look in your book. It should tell you step by step. For instance you will have asymptotes at odd multiples of \( \huge \frac{\pi}{2} \)

  37. anonymous
    • one year ago
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    Here are the properties of the tan The domain is the set of all real numbers except odd multiples of \( \huge \frac{\pi}{2} \) The range is the set of all real numbers The tangent function is an odd function, as the symmetry of the graph with respect to the origin indicates. The tangent function is periodic with period pi The x-intercepts are .....,-2pi, -pi, 0, pi, 2pi, 3pi, ..... Vertical asymptotes occur at x = odd multiples of \( \huge \frac{\pi}{2} \)

  38. anonymous
    • one year ago
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    Got it?

  39. anonymous
    • one year ago
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    Yes

  40. anonymous
    • one year ago
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    Good job. It is a lot to take in but keep practicing and you will get it.

  41. anonymous
    • one year ago
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    Thanks Nixy

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