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Math Help - Two quick Trig question I am stuck on.

  1. #1
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    Two quick Trig question I am stuck on.

    (Problem 1.)
    ---

    The equation for the angle formed by a rhythmically moving object, y, is given below, where t is time (in seconds):

    y = (1/6)(sin( ((5)(pi)(t)) / (4) )

    # or "(1/6)(sin( (5 times pi times t) divided by (4))

    (a) Solve the equation for t.
    (b) At what time(s) does the object form an angle of 0.1 radian?

    ----

    So, the first part of the problem that I do not understand is how to solve for t when there are 2 variables. Without knowing how to solve for t, I do not know how to complete the second part of the problem.

    --------------

    (Problem 2.)
    ---

    Solve each triangle ABC that exists. Angles in DMS (Degrees Minutes Seconds).
    C = 29(DEG)50(MINUTES), a = 8.61, c = 5.21

    ----

    Just some additional info to clear up some possible confusion: The lower case letters 'a' and 'c' represent triangle sides, while upper case 'C' represents the angle C across from side 'c'.

    I can get as far as finding that there are 2 triangles (ambiguous case), but I am stuck at that point.
    --------------

    Your help would be VERY greatly appreciated, thank you all in advance.
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  2. #2
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    Re: Two quick Trig question I am stuck on.

    Problem 1

    a) 6y=\sin \left(\frac{5\pi \cdot t}{4}\right) \Rightarrow \frac {5\pi \cdot t}{4}=\arcsin (6y) \Rightarrow t=\frac{4\arcsin(6y)}{5\cdot \pi}

    b) \frac{5 \pi \cdot t}{4}=0.1 \Rightarrow t=\frac{4 \cdot 0.1}{5\cdot 3.14}

    Problem 2

    \frac{a}{\sin A}=\frac{c}{\sin C}

    A+B+C=180

    b^2=a^2+c^2-2ac\cos B
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  3. #3
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    Re: Two quick Trig question I am stuck on.

    I appreciate your help, but I have a question. What happened to the 6 in 1.B?
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  4. #4
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    Re: Two quick Trig question I am stuck on.

    Quote Originally Posted by trigGirl1990 View Post
    I appreciate your help, but I have a question. What happened to the 6 in 1.B?
    Angle is represented by expression : \frac{5 \pi \cdot t}{4}

    so it doesn't matter if there is 6 or 666
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  5. #5
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    Re: Two quick Trig question I am stuck on.

    Correct me if I'm wrong, but I believe the angle is represented by 'y' in y = (1/6)(sin( ((5)(pi)(t)) / (4) ) .
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  6. #6
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    Re: Two quick Trig question I am stuck on.

    Quote Originally Posted by trigGirl1990 View Post
    Correct me if I'm wrong, but I believe the angle is represented by 'y' in y = (1/6)(sin( ((5)(pi)(t)) / (4) ) .
    We can say that \arcsin(6\cdot y)= 0.1 rad

    Do you understand now ?
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  7. #7
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    Re: Two quick Trig question I am stuck on.

    I don't see how you are getting that. The problem states "The equation for the angle formed by a rhythmically moving object, y, is given below"

    Let y = 0.1 rad
    # y never changes, it is never reassigned.
    arcsin((6)(.1)) != 0.1 rad

    It looks like you're trying to say that arcsin((6)(y)) = y

    if y = 0.1, how can y = arcsin((6)(y)) ?
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  8. #8
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    Re: Two quick Trig question I am stuck on.

    Quote Originally Posted by trigGirl1990 View Post
    I don't see how you are getting that. The problem states "The equation for the angle formed by a rhythmically moving object, y, is given below"

    Let y = 0.1 rad
    # y never changes, it is never reassigned.
    arcsin((6)(.1)) != 0.1 rad

    It looks like you're trying to say that arcsin((6)(y)) = y

    if y = 0.1, how can y = arcsin((6)(y)) ?
    You are correct I misread the question :

    1b) t=\frac{4\arcsin(6\cdot 0.1)}{5 \cdot 3.14}
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