How to Find the Value of sin 150 without a calculator?

To find the value of sin 150 degrees without a calculator, you can use trigonometric identities and knowledge of common angles.

1. Recognize the angle: 150 degrees is not one of the common angles for which we usually have exact sine values memorized. However, you can express 150 degrees as the sum of two common angles: 90 degrees and 60 degrees. So, 150 degrees can be represented as 90 degrees + 60 degrees.
   
2. Apply the sum of angles formula: Use the sum of angles formula for sine, which states that sin(A + B) = sin(A)cos(B) + cos(A)sin(B).
   Calculate: Plug in the values for A = 90 degrees and B = 60 degrees, which have known sine values of 1 and √3/2, respectively.

   sin⁡(150∘) = sin⁡(90∘+60∘) = sin⁡(90∘) cos⁡(60∘) + cos⁡(90∘) sin⁡(60∘) = (1)(32) + (0)(1/2) = √3/2

So, the value of sin 150 degrees is √3/2.