In trigonometry, Sine, Cosine and Tangent are the three major or primary ratios, which are used to find the angles and length of the triangle. Before discussing Cos 60 degrees which is equal to 1/2, let us know the importance of Cosine function in trigonometry.
Cosine function defines a relation between the adjacent side and the hypotenuse of a right-angled triangle with respect to the angle, formed between the adjacent side and the hypotenuse. Or you can say, the Cosine of angle α is equal to the ratio of the adjacent side(also called as a base) and hypotenuse of a right-angled triangle.
Also, find few important values of other trigonometric ratios:
The trigonometric functions, sin, cos and tan for an angle are the primary functions. The value for cos 60 degrees and other trigonometry ratios for all the degrees 00, 300, 450, 900,1800 are generally used in trigonometry equations. These trigonometric values are easy to memorize with the help trigonometry table.
Let us discuss the value of cos 60 degrees here in this article.
In a right-angled triangle, the cosine of ∠α is a ratio of the length of the adjacent side(base) to the ∠α and its hypotenuse, where ∠α is the angle formed between the adjacent side and the hypotenuse.
Cosine ∠α = Adjacent Side / Hypotenuse
Cos∠α = b / h
Now, to find the value of cos 60 degrees, let us consider, an equilateral triangle ABC
Here, AB=BC=AC and AD is perpendicular bisecting BC into two equal parts.
As we know, cos α = BD/AB
Let us consider the sides have 2 units, such as AB=BC=AC=2 unit and BD=CD=1 unit.
By Pythagoras theorem, in right triangle ABD,
AB2 = AD2+BD2
22 = AD2+12
AD2 = 22 -12 = 4-1= 3
Now, we have got all the sides of triangle ABD.
Therefore, the value of cos 600 = BD/AB = ½
In the same way, we can write the value of sin 600 and tan 600, as
Sin 600 = AD/AB =√3/2
Tan 600 = AD/BD = √3 / 1 = √3
Also, we can write the values of sine, cosine and tangent with respect to all the degrees in a table. We can give the values of trigonometric ratios with respect to radians equivalent to degrees, in case of a unit circle, whose radius is equal to one. The radian for a unit circle is denoted by π.
Let us draw a table with respect to degrees and radians for sine, cosine and tangent functions.
We have learned about cos 60 degrees value along with other degree’s values here, this far. Also, derived the value for sin degree and tan degrees with respect sin degrees and also in terms of radians. In the same way, we can find the values for other trigonometric ratios like secant, cosecant and cotangent.
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