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juantheron
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The value of $\sin (1^0).\sin (3^0).\sin (5^0)...\sin (87^0).\sin (89^0)$
where all angles are in degree
where all angles are in degree
jacks said:The value of $\sin (1^0).\sin (3^0).\sin (5^0)...\sin (87^0).\sin (89^0)$
where all angles are in degree
Sudharaka said:Hi jacks,
I haven't found a way solve this algebraically. But if you are interested about the answer it is, \(4.0194366942304562\times 10^{-14}\)
Follow the method used in http://www.mathhelpboards.com/showthread.php?253-Simplify-cos(a)cos(2a)cos(3a)-cos(999a)-if-a-(2pi)-1999&p=1517&viewfull=1#post1517, noting that $x=\pm1^\circ,\pm3^\circ,\pm5^\circ,\ldots,\pm89 ^\circ$ are the solutions of the equation $\cos(90x) = 0.$jacks said:The value of $\sin (1^0).\sin (3^0).\sin (5^0)...\sin (87^0).\sin (89^0)$
where all angles are in degree
The sin value of 87 degrees is approximately 0.9986, and the sin value of 89 degrees is approximately 0.9998.
The sin values of any angle can be calculated by dividing the length of the side opposite the angle by the length of the hypotenuse in a right triangle. In the case of 87 and 89 degrees, this can be done using trigonometric functions such as sine or by using a scientific calculator.
The sine function is an important tool in trigonometry as it helps to determine the relationships between angles and sides in a right triangle. It is also used in many real-world applications, such as in navigation and engineering.
Yes, the sin values of 87 and 89 degrees can also be expressed as fractions. The sin value of 87 degrees is equivalent to 499/500, and the sin value of 89 degrees is equivalent to 999/1000.
The sin values of 87 and 89 degrees are both very close to 1, which is the maximum value that the sine function can reach. This means that the angles 87 and 89 degrees are very close to being perpendicular to the hypotenuse in a right triangle, making them almost right angles.