What is the value of cosec(−π/3)?

Think it through first, then pick an option.

Answer and explanation

Correct answer: a −2/√3

cosec(−π/3) = −cosec(π/3) = −2/√3.

Why the other options are wrong

b −1/2: −1/2 is sin(−π/6), not cosec(−π/3); it is a different quantity from the one asked for.
c 1/2: 1/2 is sin(π/6); both the sign and the ratio differ.
d 2/√3: 2/√3 is positive; cosec(−θ) = −cosecθ, so the value is negative.