sin15

sin15 refers to the trigonometric function sine evaluated at an angle of 15 degrees. This value is a specific number that can be expressed in a few different ways, often involving square roots. It is a well-known trigonometric value that arises in various mathematical and physical contexts.

To derive the value of sin15, one can use trigonometric identities. For instance, it can be found by considering the difference between two standard angles, such as sin(45° - 30°). Using the sine subtraction formula, sin(A - B) = sinA cosB - cosA sinB, we can substitute A=45° and B=30°. This leads to the expression (√2/2)(√3/2) - (√2/2)(1/2), which simplifies to (√6 - √2)/4.

Alternatively, sin15 can be calculated using the half-angle formula for sine, sin(θ/2) = ±√((1 - cosθ)/2). By setting θ = 30°, we can find sin15°. Since 15° is in the first quadrant, the sine value is positive. The cosine of 30° is √3/2. Substituting this into the formula yields √((1 - √3/2)/2), which also simplifies to (√6 - √2)/4 after further algebraic manipulation. This value is approximately 0.2588.