When giving the value of a trigonometric ratio of an angle, plus the sign of another trigonometric ratio of the same angle, we can get all other trigonometric ratios of the angle.

For example. Suppose tan(B) = -3 and we know cos(B) >0.

cot(B) = 1/tan(B) = -1/3

we know that 1 + tan^2(B) = sec^2(B), so 1+ (-1/3)^2 = sec^2(B)

1 + 1/9 = sec^2(B)

sec^2(B) = 10/9

sec(B) =+/- sqrt(10)/3

since cosine is positive and tangent is negative, we know sine must be negative. Therefore, csc, which is 1/sin, is also negative.

sec(B) = sqrt(10)/3

cos(B) = 3sqrt(10)/10

sin^2(B) + cos^2(B) = 1

sin^2(B)+ 9/10 = 1

sin^2(B) = 1/10

sin(B) = -sqrt(10)/10

csc(B) = -sqrt(10)

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