The value of the trigonometric expression sin (θ/2) from π/2 < θ < π is approximately; 0.9897
We are given that;
sin θ = (2√2)/5
Condition is that; π/2 < θ < π
Now, let us try to find θ within the given boundaries;
θ = sin⁻¹((2√2)/5)
θ = sin⁻¹(0.2828)
Now, the condition π/2 < θ < π means that we are working in the second quadrant. Thus;
θ = 163.57
Thus;
sin (θ/2) = sin (163.57/2)
sin (θ/2) = 0.9897
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