Evaluate sin^-1 (a) given a=1/2?

Question

please ghelp

Answer 1

My guess is that the calculator is not the aim.

You probably should know & recognise a few really common triangles.

If sin(theta) = opposite over hypotenuse, then you need a triangle with the hypotenuse 1 & the vertical 1/2.

The horizontal side must be right for opp^2 + adj^2 = hyp^2

adj^2 = 1^2 - opp^2

= 1 - 1/4

= 3/4

adj  = sqrt(3)/2

so 1, 1/2, sqrt(3)/2 : ring any bells?

The angle is 30 degrees for this triangle.  

Draw it.

If you mirror the triangle in the x-axis you get a triangle that is 1,1,1. So it must be equilateral, so it must have angles 60, 60, 60.

Your triangle is half of this, so it must have 30, 60, 90.

The other answers give you the way to get asin(1/2) by calculator, but seeing why it's right might be more useful.

Enjoy.

Answer 2

using a scientific calculator, press:

1)  Inv / Shift

2) sin (it will turn into sin^-1)

3) input 0.5 (1/2 is also equal to 0.5)

then the answer will be 30.

Good Luck!

Answer 3

let sin^-1(a)=x

then sinx=a=1/2

or sinx=sin30 degree

x= 30 deg

or sin^-1a=30 degree where a=1/2

Answer 4

let Ó¨ = sin^(-1) (1/2)

Ө = 30° , Ө = 150°