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The graph of f(x), a trigonometric function, and the graph of g(x) = c intersect at n points over the interval 0 <= x <= 2pi. There are m algebraic solutions to the equation f(x) = g(x), where m > n. Which of the following functions are most likely to be f(x)?

f(x) = cos x
f(x) = sqrt(sin x)
f(x) = cos^2 x + cos x
f(x) = sin^2 x + cos^2 x

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2 answers
  1. Go to any number of web sites that do graphs. (a good one is wolframalpha.com)
    Take a look at the functions.
    For example, cosx intersects y=c at 1 or 2 points during one period, depending on c.
    see http://www.wolframalpha.com/input/?i=cosx

    for the last one, remember your most basic trig identity.

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  2. 1. A [ cos^2 (x) - sqrt(3)*cos(x) - 1 = 0 ]
    2. B [ f(x) = sqrt(sin x) ]
    3. D [ 7.6 hours ]
    100% ur welcome

    dirsegard this - (tagging purposes):
    1. The equation 2sin(x) + sqrt (3) cot(x) = sin(x) is partially solved below. Which of the following steps could be included in the completed solution?
    3. A buoy floats on the surface of the water. The height in meters of the buoy t hours after midnight, relative to sea level, is given by the equation f(x) = 5cos[(pi/6)t] + 4. Estimate how many hours elapse between the first two times the buoy is exactly 6 m above sea level.

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