Asked by wilson
how do you find the exact value of sin^-1(-square root of 3 divided by 2)
Answers
Answered by
Steve
better just stick with "trig"
One of the first things to do is to learn the special angles with easy trig values: 0,π/6,π/4,π/3,π/2
Knowing those, you will see that
sin π/3 = √3/2
You have -√3/2, so that means that your angle is in
QIII: π+π/3
or
QIV: 2π-π/3
Now, the inverse trig functions have principal values, and for arcsin those are -π/2 <= θ <= π/2
So, Arcsin(-√3/2) = -π/3
One of the first things to do is to learn the special angles with easy trig values: 0,π/6,π/4,π/3,π/2
Knowing those, you will see that
sin π/3 = √3/2
You have -√3/2, so that means that your angle is in
QIII: π+π/3
or
QIV: 2π-π/3
Now, the inverse trig functions have principal values, and for arcsin those are -π/2 <= θ <= π/2
So, Arcsin(-√3/2) = -π/3
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.