Trigonometry has three most important functions which are primarily used by the students to find out the unknown value of an angle and the length of the sides of a right- angled triangle. The name and abbreviations of these three functions are Sine (Sin), Cosine (Cos), Tangent (Tan). Here we will discuss Sin 60 degrees in detail. Let us first know about the importance of Sine function in Trigonometry before reviewing about Sin 60 values.

The relationship between the angle formed in a right-angle triangle and the opposite side to the angle and hypotenuse is known as Sin function.

In other words, we can say, the Sine function of angle a is the ratio of the opposite side and hypotenuse of a right-angle triangle.

Sin a = BC/AB

Sin a = a/c

The most commonly used measurement to find an unknown angle in trigonometry is radians and degrees. The degree is the most important measurement in trigonometry which is widely used.

Let us take a circle that is divided into 360 equal parts. We can take the right angle in a circle at 90°. Further, we will divide each degree into 60 minutes and minutes will be further subdivided into 60 seconds. The symbol used for the degrees, minutes and seconds are °, ‘ and ” respectively.

Minutes and Seconds are denoted as arcminutes and arcseconds.

As we know, the most commonly used primary functions of trigonometry are Sine, Cosine, and Tangent. The sin 60 degree exact value and another trigonometry ratio with different degrees such as 45°, 60°, 90°, and 180° are most commonly used in trigonometry equations. We will review sin 60 degree exact value in this article.

In Trigonometry, the sine of angle ϴ is the ratio of the length of the opposite side or perpendicular to the hypotenuse of a right-angle triangle.

On the basis of above diagram:

Sinϴ = Opposite side/ Hypotenuse

Or

Perpendicular / Hypotenuse

Perpendicular / Hypotenuse

Now we will discuss the simple procedure through which we will be able to calculate the sin 60 degree exact value and value of sine ratios for all the degrees which are commonly used. We will begin calculating the Sin values for different degrees such as Sin 0°, Sin 30°, Sin 45°, Sin 60°, and Sin 90°.

Sin 0° = √0/4 = O

Sin 30° ==√1/4= ½

Sin 45° =√2/4= ½

Sin 60° = √3/4 = √3/2

Sin 90° = √4/4 = 1

Based on the above equation, we got Sin 60 degrees value as √3/2.

Similarly, we can find the values of different degrees for cosine and tangent ratios.

We know

Sin 90° = Cos 0° =1

Sin 30° =Cos 60° = ½

Sin 60° = Cos 30° = √3/2

Sin 45°= Cos 45° = 1√2

Sin 0° = Cos 90° = 0

Also

Tan 0°, = Sin 0° / Cos 0° = 0

Tan 30° = Sin 30°/Cos 30° =1/√3

Tan 45° = Sin 45°/Cos 45° = 1

Tan 60° = Sin 60°/Cos 60° = √3

Tan 90° =Sin 90°/Cos 90° = Not defined

Trigonometry ratios with their values stated above are mentioned concerning their degrees. Similarly, we can find different values for trigonometry ratios based on radians.

1. Find the value of Sin 60 – Cos 90.

Solution:

The value of Sin 60 = √3/2

The value of Cos 90 = 0

=Sin 60 – Cos90

=√3/2 -0

= √3/2

2. Evaluate the following:

Sin 60° Cos 30° + Sin 30° Cos 60°

Solution:

The value of Sin 60 = √3/2

The value of Cos 30 = √3/2

The value of Cos 60 = ½

The value of Sin 30 = ½

Substituting the values :

Sin 60° Cos 30° - Sin 30° Cos 60°

(√3/2) x √3/2 – (1/2) x (1/2)

=√3 x √3 / 4 – 1/4

=3/4 -1/4

=2/4

=1/2

Ancient Babylonians discovered the unit of degrees and divided one revolution into 360°

The word trigonometry is derived from the Greek work Trigonon which means triangle and metrein which is known as the measure.

Aristarchus of Samos used trigonometry ratios to examine the distance between the moon and the sun

Eratosthenes Of Cyrene used trigonometry ratios to calculate Earth’s circumference

What will be the sun’s elevation if the pole of 6m high cast a shadow of 2√3 on the ground?

60°

45°

30°

90°

What will be the length of the opposite side of a right angle triangle if hypotenuse is 10mm and angle is 30?

5mm

3mm

7mm

8mm

FAQ (Frequently Asked Questions)

How will the exact value of Sin 60 degrees be calculated?

In the right angle triangle, Sin 60 value is the ratio of the length of the perpendicular side to the length of the hypotenuse.

Based on the above diagram,

The ratio of Sin 60 = Perpendicular/ Hypotenuse

The method to calculate the Sin 60 degree exact value is to divide √3 by √4 or √3/√4

With this, we got

Sin 60 value= √3 /2

So the exact value of Sin 60 degree is √3/2

In the same manner, we can calculate the value of other trigonometry ratios with different degrees.

Define Trigonometry Angles?

Trigonometry angles are the angles derived from the ratios of trigonometry functions. Trigonometry is the study of the relationship between angle and sides of a right-angle triangle. The value of the angles ranges from 0° to 360°. The widely used angles in trigonometry are 0°,.30°,45°, 60, .90°,120°,180°, 270° and 360°,. The most important trigonometry ratios which are commonly used are sine, cosine, tangent, secant, cosecant, and cotangent.

The angles used in trigonometry can be either positive or negative. The angle will be positive if it will form in a clockwise direction from the starting point and the angle will be negative if it will form in an anticlockwise direction from the starting point in the x-y plane.