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Math Help - Sine function problem

  1. #1
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    Post Sine function problem

    Here's a problem that I have to do for my pre-cal class:
    ----------------
    An architect is using a computer program to design the entrance of a railroad tunnel. The outline of the opening is modeled by the function f(x) = 8 sin x + 2, in the interval 0 ≤ x ≤ pi, where x is expressed in radians.

    Solve algebraically for all values of x in the interval 0 ≤ x ≤ pi, where the height of the opening, f(x), is 6. Express your answer in terms of pi.

    If the x-axis represents the base of the tunnel, what is the maximum height of the entrance of the tunnel?
    ----------------

    I thought I should set f(x) to 6 and solve the equation, which I did, and I got 30 as my answer. But that doesn't make sense because the answer is supposed to expressed in terms of pi, and is supposed to be less than pi. I don't know how else to solve this problem, if anyone could help that would be great! Thanks
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  2. #2
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    degrees to radians ...

    30^{\circ} = \frac{\pi}{6}

    don't forget that there is another angle where \sin{x} = \frac{1}{2} in quad II
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  3. #3
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    Quote Originally Posted by francesgw View Post
    Here's a problem that I have to do for my pre-cal class:
    ----------------
    An architect is using a computer program to design the entrance of a railroad tunnel. The outline of the opening is modeled by the function f(x) = 8 sin x + 2, in the interval 0 ≤ x ≤ pi, where x is expressed in radians.

    Solve algebraically for all values of x in the interval 0 ≤ x ≤ pi, where the height of the opening, f(x), is 6. Express your answer in terms of pi.

    If the x-axis represents the base of the tunnel, what is the maximum height of the entrance of the tunnel?
    ----------------

    I thought I should set f(x) to 6 and solve the equation, which I did, and I got 30 as my answer. But that doesn't make sense because the answer is supposed to expressed in terms of pi, and is supposed to be less than pi. I don't know how else to solve this problem, if anyone could help that would be great! Thanks
    Think pi-radians and not degrees Ya - what skeeter said!
    Last edited by Jester; January 1st 2009 at 12:15 PM. Reason: comment
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  4. #4
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    Ohhhh! Hahahah. I can't believe I forgot about converting to radians.. this problem was from a review sheet and I haven't done this type of math in a while. I'm glad I reviewed it! Thanks guys
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  5. #5
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    oh wait! what about the second part of the problem, how to find the maximum height of the tunnel? If the function was just 8 sin x then I think it would be 8, but since it's 8 sin x + 2 I'm not sure where the 2 figures in. Would that make it 10? Or I could be completely off. How do you find the max. height of the tunnel?
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  6. #6
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    what is the max value that sinx can be?
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  7. #7
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    ahhh i don't know! I don't know whether it's in degrees or radians or what.. I mean the max value of a graph of sinx would be 1.. but i don't think that's the answer you're looking for.
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  8. #8
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    okay the max value of sinx is one. So if we plug that into the equation, 8 sinx +2: 8*1+2= 10. Is the maximum 10?
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  9. #9
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    yes ... the max is 10.
    Last edited by skeeter; January 1st 2009 at 04:39 PM. Reason: messages crossed in cyberland.
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  10. #10
    Member OnMyWayToBeAMathProffesor's Avatar
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    8?

    I haven't done pre-calc in a while, but if the max value of \sin(x) is 1 then the max sin(x)+2 can be is 1, 1 \cdot8=8.
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  11. #11
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    Quote Originally Posted by OnMyWayToBeAMathProffesor View Post
    8?

    I haven't done pre-calc in a while, but if the max value of \sin(x) is 1 then the max sin(x)+2 can be is 1, 1 \cdot8=8.
    the expression is 8sinx + 2
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  12. #12
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    Edit: Sorry, you already said this. Nevermind.
    ok, the maximum value of sin(x) is one. So if we plug that into the equation, 8\sin(x)+2= 8\times1+2= 10
    Last edited by badgerigar; January 1st 2009 at 04:24 PM. Reason: Original poster had already figured it out and said it
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  13. #13
    Member OnMyWayToBeAMathProffesor's Avatar
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    I am sorry, i thought the equation was 8\sin(x+2) not 8\sin(x)+2. so 10 then?
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