Question

Evaluate arccsc sqrt 2.

Answer 1

the above answer is correct

Answer 2

{π/4 +2πn, 3π/4 +2πn}

Explanation:

csc = 1/sin, so when csc(θ) = √2, sin(θ) = 1/√2. Then θ = π/4 or 3π/4.

This means arccsc(√2) will be the set of angles shown above.

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Once you recognize that π/4 is one of the angles, you can eliminate all but the correct answer choice.

Of course this is much easier if you have memorized the short list of trig function values:

sin(π/6) = cos(π/3) = 1/2

sin(π/4) = cos(π/4) = 1/√2 = (√2)/2

sin(π/3) = cos(π/6) = (√3)/2

tan = sin/cos

sec = 1/cos

csc = 1/sin