#sin# of what is equal to #sqrt3/2#?

2 Answers
May 3, 2018

#sin60# degrees or #pi/3# radians

Explanation:

In a 30-60-90 triangle, the sides are in the ratio #x:xsqrt3:2x# (smallest leg:longest leg:hypotenuse).

#sin# is opposite side over hypotenuse

The opposite side for the #90# degree angle is the hypotenuse, so #sin90# is #1#

The opposite side for the #30# degree angle is the smallest leg (#x#).

The opposite side for the #60# degree angle is the longest leg (#xsqrt3#). #(xsqrt3)/(2x)=sqrt3/2#

May 3, 2018

#rarrx=npi+(-1)^n*(pi/3)# where #n rarrZ#

Explanation:

Let #sinx=sqrt3/2#

#rarrsinx=sin(pi/3)#

#rarrx=npi+(-1)^n*(pi/3)# where #n rarrZ#