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Hi, I need to find the domain and rnge of the following:
1. X= 1/2 (cos theta + theta sin theta)
Y=1/2 (sin theta - theta cos theta)

total guess here, but here goes
Domain cos theta = +/- 1 and domain sin theta = +/- 1 so domain theta sin theta = 0- +/-infinity
so domain of X= 1/2 (cos theta + theta sin theta) = 1/2 - +/- infinity
Then range with similar logic of Y=1/2 (sin theta - theta cos theta) = 0 - +/- infinity

Last, domain if x = cot theta

Thank yu

Range using similar logic

  • trig - ,

    As usual, the domain is the set of values for x where the function is defined.

    x = 1/2 (cosθ + θsinθ)
    domain is all real numbers.
    range is all real numbers, since θsinθ oscillates between θ and -θ.

    y = 1/2 (sinθ - θcosθ)
    same domain and range as for x

    This graph is a pair of spirals, starting at (1,0) and expanding outwards, clockwise for t<0, counterclockwise for t>0

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