Question #91cd0

1 Answer
Alan P.
Mar 30, 2017

theta = (7pi)/4+k * 2picolor(white)("XX")orcolor(white)("XX")theta =(5pi)/4+ k * 2pi
color(white)("XXXXXX") AAk in ZZ

Explanation:

Given
color(white)("XXX")sin(theta)+sqrt(2)=-sin(theta)

rarrcolor(white)("XXX")2sin(theta) = -sqrt(2)

rarrcolor(white)("XXX")sin(theta) = -sqrt(2)/2

For theta in [-pi/2,+pi/2]
rarrcolor(white)("XXX")theta=-pi/4 (or -45^@)

For theta in [0,2pi)
rarrcolor(white)("XXX")theta = (7pi)/4 or (5pi)/4

For theta unrestricted, we need to allow for integer multiples of full circles:
color(white)("XXX")theta = (7pi)/4+ k * 2pi or (5pi)/4 + k * 2pi
color(white)("XXXXXXXXX")for any integer value k

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