How do you find the exact values ofsin22.5°using the half-angle formula?
Compute the required value.
We know that, sin2θ2=1-cosθ2
Here, θ=45°
⇒ sin245°2=1-cos45°2
⇒ sin222.5°=1-cos45°2
⇒ sin222.5°=1-122
⇒ sin222.5°=2-122
⇒ sin222.5°=2-24
⇒ sin222.5°≈2-1.4144∵2≈1.414
⇒ sin222.5°≈0.15
⇒ sin22.5°≈0.15≈0.38
Hence, the value of sin22.5°is approximately 0.38.
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