How do you evaluate sin1(32) without a calculator?

2 Answers
Mar 6, 2018

60 degrees or π3 radians

Explanation:

There is no easy way to do this but through memorization. Recall that in a right triangle with angle measures 30-60-90 degrees, the side lengths are at a 1:3:2 ratio as seen below. Thus, we use the definition of sine to see that the 60 degree angle is opposite the 3 side and the hypotenuse is the 2 side. Thus, since
sin(60o)=32, sin1(32)=60o
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Mar 6, 2018

π3;2π3

Explanation:

Find arcsin(32)
sinx=32
Trig table gives as solution:
arc x=π3, or x=60
Unit circle gives another arc x that has the same sin value (sqrt3/2)
x=ππ3=2π3, or x=120