How do I determine the exact trigonometric value given CSC θ = √11/3, π/2 < θ < π; COT θ?

1 Answer
VNVDVI · Stefan V.
Feb 20, 2018

#cot(θ)=-sqrt(2)/3#

Explanation:

Recall this identity:

#1+cot^2(θ)=csc^2(θ)#

#csc^2(θ)=11/9" "# (assuming that the radical only comprises the #11#).

#1+cot^2(θ)=11/9#

#cot^2(θ)=11/9 - 9/9 = 2/9#

#cot(θ)=+-sqrt(2/9)=+- sqrt(2)/3#

We're between #π/2# and #π# (the second quadrant). Here, cosine is negative and sine is positive; thus, cotangent (cosine over sine) is negative. The negative answer is what we're looking for.

#cot(θ)=-sqrt(2)/3#

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