Question

How do I find the exact value of y=csc^-1 (-2)?

Answer 1

`y =text{arccos}(-2)` means `csc y= -2` or `sin y=-1/2` so `y = -30^circ + 360^circ k` or `y=-150^circ + 360 k,` integer `k.`

Explanation:

Pro tip: almost every "exact value" in trig involves a 30,60,90 triangle or 45,45,90 triangle.

`y = text{arccsc}(-2)`

`csc y = -2`

`1/sin y = -2`

`sin y = -1/2`

`y = -30^\circ` or `y = -150^\circ` (plus `360^\circ k`, integer `k` for completeness).