Sin vs. Cos

Difference Between Sin and Cos

Trigonometry is the field of mathematics, deals with a triangle’s sides and angles and the trigonometric functions of these angles like the sine and cosine. Both of these are the ratios of two definite sides of a right angled triangle. They help in relating the angles and sides of the triangle. They find their usage in engineering, navigation and physics.

Sine (sin)

This is the first trigonometric function which comes in use when the rise of a line segment with reference to a horizontal line in a triangle has to be calculated. The ratio between the lengths of the perpendicular to the hypotenuse of a right angled triangle is its sine value. The angle between the hypotenuse and the opposite side is denoted as θ. Therefore the sine of the angle is depicted as sin θ.

Sin θ=opposite side of triangle/hypotenuse of the triangle

The regular incidents of sound and light waves, defining the average temperature changes in a year, calculation of the length of a day, location of harmonic oscillators etc. are studied by sine. Cosecant θ is the inverse of sine θ and it is the ratio of the opposite side of a triangle to the hypotenuse.

Cosine (Cos)

This second trigonometric function helps in the calculation of “run” from the angle. It is the ratio of the base and adjacent side to the hypotenuse of a right angled triangle. It is referred as cosine θ where θ is the angle between the two sides. It is expressed as:

Cos θ = adjacent side of triangle / hypotenuse of triangle

Secant θ is the inverse of Cos θ and is the ratio between the hypotenuse and adjacent side of a triangle.


The rise in the angle can be measured by a sine function whereas Cos depicts the run with respect to an angle. If one side and two angles of a triangle are known then with the help of law of Sine, the unknown side can be measured. But if one angle and two sides are known, then to measure the other side, the law of Cosine is used. Both these functions become periodic functions of 2 π if angles more than 2π or less than -2 π are to be defined. For example, as we know 2 π radian = 360 degree;

Sin θ = Sin (θ + 2 π k)

Cos θ = Cos (θ + 2 π k)


Both sine and cosine functions hold significance in their own manner. With the help of these primary trigonometric functions, a lot mathematical problems can be solved. In terms of radian they can be depicted as:  Sin θ = Cos (π/2 – θ) and Cos θ = Sin (π/2 – θ)


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