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Math Help - (a) "Evaluate h(t) = cos (20t) for t = 3." (b) What is the value of t when h(t) =...

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    (a) "Evaluate h(t) = cos (20t) for t = 3." (b) What is the value of t when h(t) =...

    Hi there, doing some 11th grade trig I've run into difficulty. Here are the questions I'm having trouble with:

    (a) Evaluate h(t) = cos (20t) for t = 3.
    (b) What is the value of t when h(t) = 0.3 for 0 ≤ t ≤ 18?

    Answers from the book's appendix:
    (a) 1/2
    (b) 3.6, 14.4

    For (a), I get 1/2 no problem, which the book lists as the correct answer. But for (b), I only understand how to get 3.6 and not 14.4 - conceptually and practically, I'm not following how to get the 14.4 beyond a vague idea that this involves periodic values of the function.

    If you could point me in the right direction or give me a similar problem with the solution and steps for that problem, I'd really appreciate it.

    Thanks
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    Re: (a) "Evaluate h(t) = cos (20t) for t = 3." (b) What is the value of t when h(t)

    if 0 \le t \le 18 , then 0 \le 20t \le 360

    let u = 20t

    \cos(u) = 0.3

    since cos(u) = 0.3 , there is one solution in quad I and one solution in quad IV (cosine is positive in quads I and IV). note that the inverse cosine function (arccos) has a range from 0 to 90 degrees for positive values of cosine, so ...

    u = \arccos(0.3) \approx 72.5^\circ

    u = 360 - \arccos(0.3) \approx 287.5^\circ

    divide each angle above by 20 to get the values for t between 0 and 18.
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