Question

Derive trigonometric ratios of 60o....
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Answer 1

Step-by-step explanation:

Cos 90 degrees

Tan 30 degrees

Sin 30 degrees

Cos 30 degrees

Cos 0 degrees

Sin 60 degrees

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.

Cos 60 Degree Value

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.

Cos 60 Degree value

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

Cos 60 Degree

Here, AB=BC=AC and AD is perpendicular bisecting BC into two equal parts.

As we know, cos B = 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

AD =√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 60° = AD/AB = √3/2

Tan 60° = 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.

Let us draw a table with respect to degrees and radians for sine, cosine and tangent functions.