How do you evaluate arcsin(sqrt 3/2)?

3 Answers
Jun 10, 2015

arcsin(sqrt(3)/2)=60°=pi/3

Explanation:

sqrt(3)/2 is a known value, and the main angle alpha that has sin(alpha)=sqrt(3)/2 is alpha=60°=pi/3.
Because arcsin is a function RR->[-1;1], we take only the value alpha=pi/3, without the periodic values.
So arcsin(sqrt(3)/2)=60°=pi/3.

Mar 6, 2018

Make a right triangle with one side = sqrt 3 and the hypotenuse = 2 and use Pythagoras to find the other leg = 1

Explanation:

If you know that the sin 30 deg = 1/2 .............
Make a right triangle with one side = sqrt 3 and the hypotenuse = 2 and use Pythagoras to find the other leg = 1
That makes the sign of the complementary angle = 1/2 which implies the angle = 30 deg, pi/6, so
the angle in question = 90 - 30 = 60 degrees or pi / 3
OR
Just calculate (sqrt 3) / 2 and find the arcsin with a calculator

Mar 6, 2018

pi/3, (2pi)/3

Explanation:

sin x = sqrt3/2
Trig Table gives as solution:
x = pi/3 , or x = 60^@
The unit circle gives another x that has the same sin value (sqrt3/2)
x = pi - pi/3 = (2pi)/3, or x = 120^@
Answers for (0, 2pi):
pi/3, (2pi)/3
For general answer, add 2kpi