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How do you solve #csc[tan^-1 (-2)] #?

Answer 1

Asher Friedman

#csc(tan^(-1)(-2))=-sqrt5/2#

From the definition of inverse ratios, if #tan^(-1)(-2)=theta#, then #tantheta=-2#

As #tantheta=-2#, we have #cottheta=-1/2# and

#csctheta=-sqrt(1+(-1/2)^2)=-sqrt(1+1/4)#

= #-sqrt(5/4)=-sqrt5/2#

Note that as #tantheta# is negative so would be #csctheta# as domain for #theta# is #[-pi/2,pi/2]#.

hence #csctheta=csc(tan^(-1)(-2))=-sqrt5/2#

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Answer 2

Delilah Aguilar

To solve csc[tan⁻¹(-2)], first find the angle θ such that tan(θ) = -2. Then, use the reciprocal trigonometric identities to find the value of csc(θ). So, you find θ = tan⁻¹(-2) and then evaluate csc(θ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.