Asked by Grant
If sec x = -3, 0 < x < pi, find cot x.
Answers
Answered by
Reiny
sec x = -3
then cos x = -1/3, and x is in the 2nd quadrant
the triangle with angle x is in quad II and has a hypotenuse of 3 and an adjacent of 1, so the opposite is
√(9-1) = √8 or 2√2
cot x = adjacent/opposite = -1/√8
or
-√8/8 = -2√2/8 = -√2/4
then cos x = -1/3, and x is in the 2nd quadrant
the triangle with angle x is in quad II and has a hypotenuse of 3 and an adjacent of 1, so the opposite is
√(9-1) = √8 or 2√2
cot x = adjacent/opposite = -1/√8
or
-√8/8 = -2√2/8 = -√2/4
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