Sin 27 Degrees

The value of sin 27 degrees is 0.4539904. . .. Sin 27 degrees in radians is written as sin (27° × π/180°), i.e., sin (3π/20) or sin (0.471238. . .). In this article, we will discuss the methods to find the value of sin 27 degrees with examples.

• Sin 27°: 0.4539904. . .
• Sin (-27 degrees): -0.4539904. . .
• Sin 27° in radians: sin (3π/20) or sin (0.4712388 . . .)

What is the Value of Sin 27 Degrees?

The value of sin 27 degrees in decimal is 0.453990499. . .. Sin 27 degrees can also be expressed using the equivalent of the given angle (27 degrees) in radians (0.47123 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 27 degrees = 27° × (π/180°) rad = 3π/20 or 0.4712 . . .
∴ sin 27° = sin(0.4712) = 0.4539904. . .

Explanation:

For sin 27 degrees, the angle 27° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 27° value = 0.4539904. . .
Since the sine function is a periodic function, we can represent sin 27° as, sin 27 degrees = sin(27° + n × 360°), n ∈ Z.
⇒ sin 27° = sin 387° = sin 747°, and so on.
Note: Since, sine is an odd function, the value of sin(-27°) = -sin(27°).

Methods to Find Value of Sin 27 Degrees

The sine function is positive in the 1st quadrant. The value of sin 27° is given as 0.45399. . .. We can find the value of sin 27 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 27 Degrees Using Unit Circle

To find the value of sin 27 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 27° angle with the positive x-axis.
• The sin of 27 degrees equals the y-coordinate(0.454) of the point of intersection (0.891, 0.454) of unit circle and r.

Hence the value of sin 27° = y = 0.454 (approx)

Sin 27° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 27 degrees as:

• ± √(1-cos²(27°))
• ± tan 27°/√(1 + tan²(27°))
• ± 1/√(1 + cot²(27°))
• ± √(sec²(27°) - 1)/sec 27°
• 1/cosec 27°

Note: Since 27° lies in the 1st Quadrant, the final value of sin 27° will be positive.

We can use trigonometric identities to represent sin 27° as,

• sin(180° - 27°) = sin 153°
• -sin(180° + 27°) = -sin 207°
• cos(90° - 27°) = cos 63°
• -cos(90° + 27°) = -cos 117°

☛ Also Check:

• sin 30 degrees
• sin 120 degrees
• sin 50 degrees
• sin 66 degrees
• sin 100 degrees
• sin 39 degrees

FAQs on Sin 27 Degrees

What is Sin 27 Degrees?

Sin 27 degrees is the value of sine trigonometric function for an angle equal to 27 degrees. The value of sin 27° is 0.454 (approx).

How to Find the Value of Sin 27 Degrees?

The value of sin 27 degrees can be calculated by constructing an angle of 27° with the x-axis, and then finding the coordinates of the corresponding point (0.891, 0.454) on the unit circle. The value of sin 27° is equal to the y-coordinate (0.454). ∴ sin 27° = 0.454.

What is the Value of Sin 27° in Terms of Sec 27°?

Since the sine function can be represented using the secant function, we can write sin 27° as √(sec²(27°) - 1)/sec 27°. The value of sec 27° is equal to 1.122326.

What is the Value of Sin 27 Degrees in Terms of Cos 27°?

Using trigonometric identities, we can write sin 27° in terms of cos 27° as, sin(27°) = √(1-cos²(27°)). Here, the value of cos 27° is equal to 0.8910065.

How to Find Sin 27° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 27° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(27°))
• ± tan 27°/√(1 + tan²(27°))
• ± 1/√(1 + cot²(27°))
• ± √(sec²(27°) - 1)/sec 27°
• 1/cosec 27°

☛ Also check: trigonometric table