Sin 51 Degrees

The value of sin 51 degrees is 0.7771459. . .. Sin 51 degrees in radians is written as sin (51° × π/180°), i.e., sin (17π/60) or sin (0.890117. . .). In this article, we will discuss the methods to find the value of sin 51 degrees with examples.

• Sin 51°: 0.7771459. . .
• Sin (-51 degrees): -0.7771459. . .
• Sin 51° in radians: sin (17π/60) or sin (0.8901179 . . .)

What is the Value of Sin 51 Degrees?

The value of sin 51 degrees in decimal is 0.777145961. . .. Sin 51 degrees can also be expressed using the equivalent of the given angle (51 degrees) in radians (0.89011 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 51 degrees = 51° × (π/180°) rad = 17π/60 or 0.8901 . . .
∴ sin 51° = sin(0.8901) = 0.7771459. . .

Explanation:

For sin 51 degrees, the angle 51° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 51° value = 0.7771459. . .
Since the sine function is a periodic function, we can represent sin 51° as, sin 51 degrees = sin(51° + n × 360°), n ∈ Z.
⇒ sin 51° = sin 411° = sin 771°, and so on.
Note: Since, sine is an odd function, the value of sin(-51°) = -sin(51°).

Methods to Find Value of Sin 51 Degrees

The sine function is positive in the 1st quadrant. The value of sin 51° is given as 0.77714. . .. We can find the value of sin 51 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 51° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 51 degrees as:

• ± √(1-cos²(51°))
• ± tan 51°/√(1 + tan²(51°))
• ± 1/√(1 + cot²(51°))
• ± √(sec²(51°) - 1)/sec 51°
• 1/cosec 51°

Note: Since 51° lies in the 1st Quadrant, the final value of sin 51° will be positive.

We can use trigonometric identities to represent sin 51° as,

• sin(180° - 51°) = sin 129°
• -sin(180° + 51°) = -sin 231°
• cos(90° - 51°) = cos 39°
• -cos(90° + 51°) = -cos 141°

Sin 51 Degrees Using Unit Circle

To find the value of sin 51 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 51° angle with the positive x-axis.
• The sin of 51 degrees equals the y-coordinate(0.7771) of the point of intersection (0.6293, 0.7771) of unit circle and r.

Hence the value of sin 51° = y = 0.7771 (approx)

☛ Also Check:

• sin 120 degrees
• sin 15 degrees
• sin 13 degrees
• sin 83 degrees
• sin 585 degrees
• sin 145 degrees

FAQs on Sin 51 Degrees

What is Sin 51 Degrees?

Sin 51 degrees is the value of sine trigonometric function for an angle equal to 51 degrees. The value of sin 51° is 0.7771 (approx).

What is the Value of Sin 51 Degrees in Terms of Cos 51°?

Using trigonometric identities, we can write sin 51° in terms of cos 51° as, sin(51°) = √(1-cos²(51°)). Here, the value of cos 51° is equal to 0.6293203.

How to Find Sin 51° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 51° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(51°))
• ± tan 51°/√(1 + tan²(51°))
• ± 1/√(1 + cot²(51°))
• ± √(sec²(51°) - 1)/sec 51°
• 1/cosec 51°

☛ Also check: trigonometric table

How to Find the Value of Sin 51 Degrees?

The value of sin 51 degrees can be calculated by constructing an angle of 51° with the x-axis, and then finding the coordinates of the corresponding point (0.6293, 0.7771) on the unit circle. The value of sin 51° is equal to the y-coordinate (0.7771). ∴ sin 51° = 0.7771.

What is the Value of Sin 51° in Terms of Cosec 51°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 51° as 1/cosec(51°). The value of cosec 51° is equal to 1.28675.