Sin 31 Degrees

The value of sin 31 degrees is 0.5150380. . .. Sin 31 degrees in radians is written as sin (31° × π/180°), i.e., sin (0.541052. . .). In this article, we will discuss the methods to find the value of sin 31 degrees with examples.

• Sin 31°: 0.5150380. . .
• Sin (-31 degrees): -0.5150380. . .
• Sin 31° in radians: sin (0.5410520 . . .)

What is the Value of Sin 31 Degrees?

The value of sin 31 degrees in decimal is 0.515038074. . .. Sin 31 degrees can also be expressed using the equivalent of the given angle (31 degrees) in radians (0.54105 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 31 degrees = 31° × (π/180°) rad = 0.5410 . . .
∴ sin 31° = sin(0.5410) = 0.5150380. . .

Explanation:

For sin 31 degrees, the angle 31° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 31° value = 0.5150380. . .
Since the sine function is a periodic function, we can represent sin 31° as, sin 31 degrees = sin(31° + n × 360°), n ∈ Z.
⇒ sin 31° = sin 391° = sin 751°, and so on.
Note: Since, sine is an odd function, the value of sin(-31°) = -sin(31°).

Methods to Find Value of Sin 31 Degrees

The sine function is positive in the 1st quadrant. The value of sin 31° is given as 0.51503. . .. We can find the value of sin 31 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 31° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 31 degrees as:

• ± √(1-cos²(31°))
• ± tan 31°/√(1 + tan²(31°))
• ± 1/√(1 + cot²(31°))
• ± √(sec²(31°) - 1)/sec 31°
• 1/cosec 31°

Note: Since 31° lies in the 1st Quadrant, the final value of sin 31° will be positive.

We can use trigonometric identities to represent sin 31° as,

• sin(180° - 31°) = sin 149°
• -sin(180° + 31°) = -sin 211°
• cos(90° - 31°) = cos 59°
• -cos(90° + 31°) = -cos 121°

Sin 31 Degrees Using Unit Circle

To find the value of sin 31 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 31° angle with the positive x-axis.
• The sin of 31 degrees equals the y-coordinate(0.515) of the point of intersection (0.8572, 0.515) of unit circle and r.

Hence the value of sin 31° = y = 0.515 (approx)

☛ Also Check:

• sin 150 degrees
• sin 556 degrees
• sin 360 degrees
• sin 200 degrees
• sin 78 degrees
• sin 910 degrees

FAQs on Sin 31 Degrees

What is Sin 31 Degrees?

Sin 31 degrees is the value of sine trigonometric function for an angle equal to 31 degrees. The value of sin 31° is 0.515 (approx).

How to Find the Value of Sin 31 Degrees?

The value of sin 31 degrees can be calculated by constructing an angle of 31° with the x-axis, and then finding the coordinates of the corresponding point (0.8572, 0.515) on the unit circle. The value of sin 31° is equal to the y-coordinate (0.515). ∴ sin 31° = 0.515.

What is the Value of Sin 31 Degrees in Terms of Cot 31°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 31° can be written as 1/√(1 + cot²(31°)). Here, the value of cot 31° is equal to 1.66427.

How to Find Sin 31° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 31° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(31°))
• ± tan 31°/√(1 + tan²(31°))
• ± 1/√(1 + cot²(31°))
• ± √(sec²(31°) - 1)/sec 31°
• 1/cosec 31°

☛ Also check: trigonometry table

What is the Value of Sin 31° in Terms of Cosec 31°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 31° as 1/cosec(31°). The value of cosec 31° is equal to 1.94160.