How do you find inverse sin (-1/2)?

2 Answers
Oct 10, 2015

210°, 330°

Explanation:

Using your calculator, press "shift" "sin (1/2)" and it will give you 30. (Always ignore the negative when you are doing the inverse!)

But since this is a negative, you cannot just write 30° as your final answer.

Using the ASTC rule, you know that for sin to be positive it has to be in Quadrant 1 and 2. But since this is a negative it has to be the complete opposite! So Quadrant 3 and 4 is where sin will be negative.

In Quadrant 3, from the ASTC rule, take 180°+prop rArr prop being the answer you just got aka 30°!

In Quadrant 4, from the ASTC rule, take 360°-prop .

So,

180°+30°=210°
360°-30°=330°

Oct 10, 2015

We use our knowledge of special angles together with the definition of inverse sine.

Explanation:

"inverse sine" may refer to either a single values function (the principal value -- common in introductory courses) or to a "multivalued function".

Here is the definition for the principal value:

y=arcsinx if and only if (-pi/2 <= y <= pi/2 bb" and " siny=x)

We know that sin(pi/6) = 1/2 and so, sin(-pi/6) = -1/2.

Therefore, the (principal) inverse sine of -1/2 is -pi/6.