Posted by Courtney on .
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
Range using similar logic
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