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

3 Answers
Jun 10, 2015

Answer:

#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

Answer:

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

Answer:

#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#