The principal value of sin inverse (-1/2) is:
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Answer:
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
°
+
∝
⇒
∝
being the answer you just got aka
30
°
!
In Quadrant 4, from the ASTC rule, take
360
°
−
∝
.
So,
180
°
+
30
°
=
210
°
360
°
−
30
°
=
330
Step-by-step explanation:
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