Question

Find the exact value of sin-1 the quantity square root of three divided by two

Answer 1

Answer is 60 degrees.

Explanation:

We know that in a right angled triangle if one leg is 1, and hypotenuse is 2,

then other leg =
`√(2^2-1^2 ) =√(3)`

(By using Pythagorean theotrem)

Now consider a right angle triangle with hypotenuse 2 and one leg 1, and the angle between other leg and hypotenuse.

Since sin 30 = 1/2 we have cos 60= sin (90-60) = 1/2

Hence sin 60 = rt 3 /2

Using the above we get sin inverse of quantity square root of three divided by two is 60 degrees.