Question

An angle theta satisfies the relation (csc theta)(cos theta)=-1

Give an example of information needed to determine a unique value for theta
If sec theta is known to be negative, what is the csc theta value of theta?
cscØ cosØ = -1
(1/sinØ)(cosØ) = -1
cotØ = -1
tanØ = -1, I know tan45° = +1
so Ø is in quadrants II or IV
Ø = 180-45 = 135°
or
Ø = 360-45 = 315°

so the additional information would have to be:
in which quadrant is the angle in.

sinØ = 1/√2 if Ø = 135
sinØ = -1/√2 if Ø = 315

so cscØ = √2 in II and cscØ = -√2 in IV
An angle theta satisfies the relation (csc theta)(cos theta)=-1

Give an example of information needed to determine a unique value for theta
If sec theta is known to be negative, what is the csc theta value of theta?

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