Exact Value Of Sin 120

In Mathematics, trigonometry is a branch that deals with the study of measures of right-angle triangles such as length, pinnacle and angles. Trigonometry has enormous applications in diverse fields, such every bit Architecture, Navigation systems, sound waves detections, so on. In this article, let us discuss the value of sin 120, and the diverse methods which are used to observe the sin 120 values using other trigonometric angles and identities are explained in particular. Also, go through the below-provided commodity to learn all the sine values.

Sin 0
Sin 30 degrees
Sin 45 Degrees
Sin 60 Degrees
Sin 90 Degrees

How to Derive the Value of Sin 120 Degrees?

The sin 120-degrees value can be identified using either unit of measurement circle or with the aid of other trigonometric angles such every bit 60, 180 degrees and so on. Let usa consider the value 120 degrees in the cartesian plane. Nosotros know that the cartesian plane is divided into 4 quadrants. The value 120 degrees falls on the second quadrant. Every bit the value of sine function in the 2d quadrant takes the positive value, the value of sin 120 degrees should be a positive value.
Sin 120 values

By using the unit circle, the value of sin 120 can be calculated. We know the radius of the circle is the hypotenuse of the right triangle which is equal to the value 1. From the cartesian plane, nosotros take, x= cos and y = sin

By looking at the diagram given above, the value of sin sixty is equal to the value of sin 120.

Information technology ways that, sin lx = sin 120 = √3/2.

Method one

Some other method to find the value of sin 120 degrees is past using the other angles of the sine functions such as threescore degrees and 180 degrees which are taken from the trigonometry table.

Nosotros know that

180° – 60° = 120°

As well, nosotros know that the trigonometric identity sin (180°- a ) = sin a

Now,

Sin ( 180°- 120°) = sin 120°

Therefore, sin 120°= sin lx°

From the trigonometry table, use the value of sin lx° which is equal to √three/2.

Hence, the value of sin 120 degrees is √iii/2

Method ii

By using the value of cosine function relations, nosotros can easily discover the value of sin 120 degrees.

Using the trigonometry formula, sin (90 + a) = cos a, nosotros can find the sin 120 value.

Every bit given, sin (90° +30°) = cos 30°

Information technology means that sin 120° = cos 30°

We know that the value of cos thirty degrees is √iii/ii.

Therefore, sin 120° = √3/ii.

Hither, the values of other of import trigonometric angles for different ratios are provided here for the reference.

Trigonometry Ratio Table
Angles (In Degrees)	0	thirty	45	60	90	180	270	360
Angles (In Radians)	0	π/half-dozen	π/4	π/3	π/ii	π	3π/2	2π
sin	0	1/2	1/√2	√3/two	ane	0	−1	0
cos	1	√3/two	one/√ii	i/2	0	−i	0	ane
tan	0	1/√three	1	√3	Not Divers	0	Non Defined	1
cot	Non Defined	√3	1	1/√3	0	Not Divers	0	Not Divers
cosec/csc	Non Divers	2	√2	ii/√iii	1	Not Divers	−one	Non Defined
sec	one	2/√3	√2	2/√three	Not Divers	−i	Not Defined	ane