Sin vs Cos
The branch of mathematics, which deals with sides and angles of triangle and trigonometric functions of these angles is called trigonometry. The basic trigonometric functions of an angle are sine (sin) and cosine (cos) of that angle. Trigonometric sin and cos are ratios of two specific sides in right angle triangle and useful in relating angles and sides of triangles. The use of these trigonometric sin and cos has been rapidly increased in resolving engineering, navigation and physics problems.
Sine (Sin)
Sine is the first trigonometric function. Trigonometric Sine is used to calculate the “rise” of a line segment with respect to horizontal line in a given triangle. For a right angle triangle, sine of an angle is the ratio of length of perpendicular or opposite side to hypotenuse. It is expressed in terms of sine θ, where θ is the angle between opposite side and hypotenuse. Sine θ is abbreviated as sin θ. In terms of expression
Sin θ = opposite side of triangle / hypotenuse of triangle.
Trigonometric sine is used in studying the periodic phenomena of sound and light waves, determining the average temperature variations during the whole year, calculating day length, position of harmonic oscillators and many more. The inverse of sine θ is cosecant θ. Cosecant θ is the ratio of hypotenuse to opposite side of a triangle and abbreviated as Cosec θ.
Cosine (Cos)
Cosine is the second trigonometric function. With respect of a horizontal line, cosine is used to calculate “run” from the angle. For a right angle triangle, cosine of an angle is the ratio of base or adjacent side to hypotenuse of triangle. This term is expressed as cosine θ, where θ is the angle between adjacent side and hypotenuse. Cosine θ is abbreviated as Cos θ. In terms of expression
Cos θ = adjacent side of triangle / hypotenuse of triangle
The inverse of Cos θ is secant θ. Secant θ is the ratio of hypotenuse to adjacent side of a triangle. Secant θ is abbreviated as Sec θ.
Comparison
• If the length of a line segment is 1 cm, sine tells the rise with respect to an angle, while for the same length of line, Cos tells the run with respect to an angle.
• Law of Sine is used to calculate the length of unknown side of that triangle, whose one side and two angles are known. Whereas the law of Cosine is used to calculate the side of that triangle, whose one angle and two sides are known.
• As 2 π radian = 360 degree, so if we want to calculate the values of Sin and Cos for angle greater than 2 π or less than -2 π, then Sin and Cosine are periodic functions of 2 π. Like
Sin θ = Sin (θ + 2 π k)
Cos θ = Cos (θ + 2 π k)
Conclusion
Sine and cosine are primary trigonometric functions; however, each function has its own importance in resolving mathematics problems. However, If we express sine and cosine in term of radian, we can correlate these two trigonometric identities in terms of radian is
Sin θ = Cos (π/2 – θ) and Cos θ = Sin (π/2 – θ)