Sin 120: Derive the Value of Sin 120 Degrees? Method 1 or 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

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

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

Derive the Value of Sin 120 Degrees?

The sin 120-degrees value can be identified using either unit circle or with the help of other trigonometric angles such as 60,180 degrees and so on. consider the value 120 degrees in the cartesian plane. We know that the cartesian plane is divided into four quadrants. The value 120 degrees falls on the second quadrant. As the value of sine function in the second quadrant takes the positive value, the value of sin 120 degrees should be a positive value.

Derive the Value of Sin 120

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, we take, x = cos and y = sin

By looking at the diagram given above, the value of sin 60 is equal to the value of sin 120.

It means that,

Method 1

Another method to find the value of is by using the other angles of the sine functions such as and which are taken from the trigonometry table.

We know that

Also, we know that the trigonometric identity

Now,

Therefore,

From the trigonometry table, use the value of s which is equal to

Hence, the value of is

Method 2

By using the value of cosine function relations, we can easily find the value of sin 120 degrees.

Using the trigonometry formula, we can find the sin 120 value.

As given, °

It means that

We know that the value of is .

Therefore,

By Using the Value of Cosine Function Relations, We Can Easily Find the Value of Sin 120 Degrees
Angles (In Degree)
Angles (In Radians)
sin
cos
tanNot definedNot defined
cotNot DefinedNot definedNot Defined
cosec/cscNot DefinedNot definedNot Defined
secNot DefinedNot defined

Here, the values of other important trigonometric angles for different ratios are provided here for the reference.

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