Sin 55 Degrees

The value of sin 55 degrees is 0.8191520. . .. Sin 55 degrees in radians is written as sin (55° × π/180°), i.e., sin (11π/36) or sin (0.959931. . .). In this article, we will discuss the methods to find the value of sin 55 degrees with examples.

• Sin 55°: 0.8191520. . .
• Sin (-55 degrees): -0.8191520. . .
• Sin 55° in radians: sin (11π/36) or sin (0.9599310 . . .)

What is the Value of Sin 55 Degrees?

The value of sin 55 degrees in decimal is 0.819152044. . .. Sin 55 degrees can also be expressed using the equivalent of the given angle (55 degrees) in radians (0.95993 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 55 degrees = 55° × (π/180°) rad = 11π/36 or 0.9599 . . .
∴ sin 55° = sin(0.9599) = 0.8191520. . .

Explanation:

For sin 55 degrees, the angle 55° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 55° value = 0.8191520. . .
Since the sine function is a periodic function, we can represent sin 55° as, sin 55 degrees = sin(55° + n × 360°), n ∈ Z.
⇒ sin 55° = sin 415° = sin 775°, and so on.
Note: Since, sine is an odd function, the value of sin(-55°) = -sin(55°).

Methods to Find Value of Sin 55 Degrees

The sine function is positive in the 1st quadrant. The value of sin 55° is given as 0.81915. . .. We can find the value of sin 55 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 55° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 55 degrees as:

• ± √(1-cos²(55°))
• ± tan 55°/√(1 + tan²(55°))
• ± 1/√(1 + cot²(55°))
• ± √(sec²(55°) - 1)/sec 55°
• 1/cosec 55°

Note: Since 55° lies in the 1st Quadrant, the final value of sin 55° will be positive.

We can use trigonometric identities to represent sin 55° as,

• sin(180° - 55°) = sin 125°
• -sin(180° + 55°) = -sin 235°
• cos(90° - 55°) = cos 35°
• -cos(90° + 55°) = -cos 145°

Sin 55 Degrees Using Unit Circle

To find the value of sin 55 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 55° angle with the positive x-axis.
• The sin of 55 degrees equals the y-coordinate(0.8192) of the point of intersection (0.5736, 0.8192) of unit circle and r.

Hence the value of sin 55° = y = 0.8192 (approx)

☛ Also Check:

• sin 90 degrees
• sin 270 degrees
• sin 36 degrees
• sin 72 degrees
• sin 95 degrees
• sin 25 degrees

FAQs on Sin 55 Degrees

What is Sin 55 Degrees?

Sin 55 degrees is the value of sine trigonometric function for an angle equal to 55 degrees. The value of sin 55° is 0.8192 (approx).

What is the Value of Sin 55 Degrees in Terms of Cos 55°?

Using trigonometric identities, we can write sin 55° in terms of cos 55° as, sin(55°) = √(1-cos²(55°)). Here, the value of cos 55° is equal to 0.5735764.

How to Find Sin 55° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 55° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(55°))
• ± tan 55°/√(1 + tan²(55°))
• ± 1/√(1 + cot²(55°))
• ± √(sec²(55°) - 1)/sec 55°
• 1/cosec 55°

☛ Also check: trigonometric table

How to Find the Value of Sin 55 Degrees?

The value of sin 55 degrees can be calculated by constructing an angle of 55° with the x-axis, and then finding the coordinates of the corresponding point (0.5736, 0.8192) on the unit circle. The value of sin 55° is equal to the y-coordinate (0.8192). ∴ sin 55° = 0.8192.

What is the Value of Sin 55° in Terms of Cosec 55°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 55° as 1/cosec(55°). The value of cosec 55° is equal to 1.22077.