put sin(15) in the calculator and it will give you something .65 like that
The exact value of sin (15°) is 0.795. For every angle, the sin function has a unique value.
The field of mathematics is concerned with the relationships between triangles' sides and angles, as well as the related functions of any angle.
The value of the sin 15 is obtained with the help of sin 30 as;
(Sin A/2 + Cos B/2)² = Sin²(A/2) + Cos²(B/2) +2 Sin(A/2)Cos(B/2)
(Sin A/2 + Cos B/2)² = = 1 + SIN A
Sin P/2 + Cos P/2 = ± √ (1 + sin A)
Data taken:
A = 30°
A/2 = 30/2
A/2=15°
Substitute values:
Sin 15° + Cos 15° = ±√ (1 + sin 30) …(1)
(Sin A/2 – Cos B/2)² = Sin²(A/2) + Cos²(B/2) – 2 Sin(A/2)Cos(B/2)
(Sin A/2 – Cos B/2)² == 1 – SIN A
Sin A/2 – Cos B/2 = ± √(1 – sin A)
Substitute the values we get;
Sin 15° – Cos 15° = ±√(1 – sin 30°)
If value of sin 15° and cos 15° is grater than zero. Their sum will also grater than zero.
Sin 15° + Cos 15° > 0
Sin 15° + Cos 15° = √(1 + Sin 30°)
Sin 15° – Cos 15° = √2 (1/√2 Sin 15˚ – 1/√2 Cos 15˚)
Sin 15° – Cos 15° = √2 (Cos 45° Sin 15˚ – Sin 45° Cos 15°)
Sin 15° – Cos 15° = √2 Sin (15˚ – 45˚)
Sin 15° – Cos 15° = √2 Sin (- 30˚)
Sin 15° – Cos 15° = -√2 Sin 30°
Sin 15° – Cos 15° = -√2 x 1/2
Sin 15° – Cos 15° = – √2/2
So, sin 15° – cos 15° < 0
Sin 15° – Cos 15°= -√(1 – Sin 30°)
2 Sin 15° = √(1 + ½) – √(1 – ½)
2 Sin 15° = (√3−1)/√2
Sin 15° = (√3−1)/2√2
Sin 15° = 0.795
Hence,0.795 is the correct answer for the sin (15°).
To learn more about trigonometry, refer to the link:
https://brainly.com/question/26719838
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