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Math Help - Need help with trig graph questions

  1. #1
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    Need help with trig graph questions

    Hi, there are a few trig questions I'm not sure how to work out:

    The equation y = a cos bx can be used to describe some natural cycles, such as tides and the phases of the moon.

    1] Determine the constants a and b and write the equation representing the scenario.

    a) A 12 hour gap between high tides of 2.3m and low tides of -2.3m
    b) Same as a), except tides vary from 0.7m to 5.3m.

    2] State the greatest possible value of 2sin(x - 30 deg) and the smallest possible value of x that will get this maximum value.

    3] State the period, amplitude and range of this equation: y = -2sin(x - 45 deg) + 2

    Thanks in advance for help, and please explain your working. Thanks!
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  2. #2
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    Hello BG5965
    Quote Originally Posted by BG5965 View Post
    Hi, there are a few trig questions I'm not sure how to work out:

    The equation y = a cos bx can be used to describe some natural cycles, such as tides and the phases of the moon.

    1] Determine the constants a and b and write the equation representing the scenario.

    a) A 12 hour gap between high tides of 2.3m and low tides of -2.3m
    b) Same as a), except tides vary from 0.7m to 5.3m.

    2] State the greatest possible value of 2sin(x - 30 deg) and the smallest possible value of x that will get this maximum value.

    3] State the period, amplitude and range of this equation: y = -2sin(x - 45 deg) + 2

    Thanks in advance for help, and please explain your working. Thanks!
    What you need to know about the graph of the equation y = a\cos bx:
    Amplitude: y varies between +a and -a. The value of a is called the amplitude of the graph.

    Period: the distance between corresponding points on consecutive cycles - for instance two consecutive peak values - is called the period. If x is measured in degrees, the period is \frac{360}{b}.

    Initial value. When x = 0, y = a. So the graph starts at its maximum value.
    1 a) The 12-hour gap between consecutive high tides gives the value of the period. So using the formula for the period above:
    \frac{360}{b}=12

    \Rightarrow b = ... ?
    The maximum and minimum values are +2.3 and -2.3, so the value of a is ... ?

    b) Here the values vary between 0.7 and 5.3, a difference of 4.6. You'll notice that these values are exactly 3 more than the values in (a). So

    • the amplitude is still 2.3, but


    • you'll need to add a constant value of 3 to the equation in (a). Answer: y = a\cos bx + 3 (with the same values of a and b as before)

    2) The sine function again takes values between +1 and -1, with its first maximum occurring at 90^o. So 2\sin(x-30^o) varies between +2 and -2, with the first maximum occurring when x-30 = 90 \Rightarrow x = ... ?

    3) Use the same ideas again to get the answers here.

    Can you fill in the gaps?

    Grandad
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