Sin 144 Degrees

The value of sin 144 degrees is 0.5877852. . .. Sin 144 degrees in radians is written as sin (144° × π/180°), i.e., sin (4π/5) or sin (2.513274. . .). In this article, we will discuss the methods to find the value of sin 144 degrees with examples.

• Sin 144°: 0.5877852. . .
• Sin (-144 degrees): -0.5877852. . .
• Sin 144° in radians: sin (4π/5) or sin (2.5132741 . . .)

What is the Value of Sin 144 Degrees?

The value of sin 144 degrees in decimal is 0.587785252. . .. Sin 144 degrees can also be expressed using the equivalent of the given angle (144 degrees) in radians (2.51327 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 144 degrees = 144° × (π/180°) rad = 4π/5 or 2.5132 . . .
∴ sin 144° = sin(2.5132) = 0.5877852. . .

Explanation:

For sin 144 degrees, the angle 144° lies between 90° and 180° (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 144° value = 0.5877852. . .
Since the sine function is a periodic function, we can represent sin 144° as, sin 144 degrees = sin(144° + n × 360°), n ∈ Z.
⇒ sin 144° = sin 504° = sin 864°, and so on.
Note: Since, sine is an odd function, the value of sin(-144°) = -sin(144°).

Methods to Find Value of Sin 144 Degrees

The sine function is positive in the 2nd quadrant. The value of sin 144° is given as 0.58778. . .. We can find the value of sin 144 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 144° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 144 degrees as:

• ± √(1-cos²(144°))
• ± tan 144°/√(1 + tan²(144°))
• ± 1/√(1 + cot²(144°))
• ± √(sec²(144°) - 1)/sec 144°
• 1/cosec 144°

Note: Since 144° lies in the 2nd Quadrant, the final value of sin 144° will be positive.

We can use trigonometric identities to represent sin 144° as,

• sin(180° - 144°) = sin 36°
• -sin(180° + 144°) = -sin 324°
• cos(90° - 144°) = cos(-54°)
• -cos(90° + 144°) = -cos 234°

Sin 144 Degrees Using Unit Circle

To find the value of sin 144 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 144° angle with the positive x-axis.
• The sin of 144 degrees equals the y-coordinate(0.5878) of the point of intersection (-0.809, 0.5878) of unit circle and r.

Hence the value of sin 144° = y = 0.5878 (approx)

☛ Also Check:

• sin 120 degrees
• sin 53 degrees
• sin 360 degrees
• sin 67 degrees
• sin 31 degrees
• sin 44 degrees

FAQs on Sin 144 Degrees

What is Sin 144 Degrees?

Sin 144 degrees is the value of sine trigonometric function for an angle equal to 144 degrees. The value of sin 144° is 0.5878 (approx).

How to Find the Value of Sin 144 Degrees?

The value of sin 144 degrees can be calculated by constructing an angle of 144° with the x-axis, and then finding the coordinates of the corresponding point (-0.809, 0.5878) on the unit circle. The value of sin 144° is equal to the y-coordinate (0.5878). ∴ sin 144° = 0.5878.

What is the Value of Sin 144 Degrees in Terms of Tan 144°?

We know, using trig identities, we can write sin 144° as -tan 144°/√(1 + tan²(144°)). Here, the value of tan 144° is equal to -0.726542.

How to Find Sin 144° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 144° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(144°))
• ± tan 144°/√(1 + tan²(144°))
• ± 1/√(1 + cot²(144°))
• ± √(sec²(144°) - 1)/sec 144°
• 1/cosec 144°

☛ Also check: trigonometry table

What is the Exact Value of sin 144 Degrees?

The exact value of sin 144 degrees can be given accurately up to 8 decimal places as 0.58778525.