Sin, Cos and Tan is the formula for sine. A right-angled triangle is a triangle in which one of the angles is a right-angle. The hypotenuse of a right angled triangle is the longest side, which is the one opposite the right angle. The adjacent side is the side which is between the angle in question and the right angle.
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There is no easy formula. You need to go into McLaurin's Theorem. .
Visually if you have a circle of '1' radius centred on the origin (0,0)
When that radius makes an angle of 30 degrees, with x-axis , then the height of the chord from the x-axis to the point where the radius touches the circle is 1/2 the radial length.
Hence Sine(30 degrees) = 1/2 = 0.5.
All the other angles can be found, by sweeping the radius about the x-axis for an angular value, and the chord length is the Sine value.
Sine= Opposite/ Hypotenuse Cosine= Adjacent/ Hypotenuse
Sine (0) = 0 Sin(30) = 0.5 Sin(45) = 0.7071... Sin(60) = 0.8660.... Sin(90) = 1 Are just a few of the Sine(Trigonometric) values.
√ 1/2 = sine(45)= cosine(45) -Key
0.602
In a right angle triangle divide the opposite by the hypotenuse to find the sine ratio.