Question

find value of sin 22

Answer 1

0.374607 is value of sin22°

Answer 2

22½° lies in the first quadrant.

Therefore, sin 22½° is positive.

For all values of the angle A we know that,cos A = 1 - 2 sin2 A2

1 - cos A = 2 sin22 A2A2

⇒ 2 sin22 A2A2 = 1 - cos A

⇒ 2 sin22 22½˚ = 1 - cos 45°

⇒ sin22 22½˚ = 1−cos45°21−cos45°2

⇒ sin22 22½˚ = 1−12√21−122, [Since we know cos 45° = 1√21√2]

⇒ sin 22½˚ = 12(1−12√)−−−−−−−−√12(1−12), [Since, sin 22½˚ > 0]

⇒ sin 22½˚ = 2√−122√−−−−√2−122

⇒ sin 22½˚ = 122−2–√−−−−−−√122−2

Therefore, sin 22½˚ = 122−2–√−−−−−−√