Sin 1 Degrees

The value of sin 1 degrees is 0.0174524. . .. Sin 1 degrees in radians is written as sin (1° × π/180°), i.e., sin (0.017453. . .). In this article, we will discuss the methods to find the value of sin 1 degrees with examples.

• Sin 1°: 0.0174524. . .
• Sin (-1 degrees): -0.0174524. . .
• Sin 1° in radians: sin (0.0174532 . . .)

What is the Value of Sin 1 Degrees?

The value of sin 1 degrees in decimal is 0.017452406. . .. Sin 1 degrees can also be expressed using the equivalent of the given angle (1 degrees) in radians (0.01745 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 1 degrees = 1° × (π/180°) rad = 0.0174 . . .
∴ sin 1° = sin(0.0174) = 0.0174524. . .

Explanation:

For sin 1 degrees, the angle 1° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 1° value = 0.0174524. . .
Since the sine function is a periodic function, we can represent sin 1° as, sin 1 degrees = sin(1° + n × 360°), n ∈ Z.
⇒ sin 1° = sin 361° = sin 721°, and so on.
Note: Since, sine is an odd function, the value of sin(-1°) = -sin(1°).

Methods to Find Value of Sin 1 Degrees

The sine function is positive in the 1st quadrant. The value of sin 1° is given as 0.01745. . .. We can find the value of sin 1 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 1° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 1 degrees as:

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

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

We can use trigonometric identities to represent sin 1° as,

• sin(180° - 1°) = sin 179°
• -sin(180° + 1°) = -sin 181°
• cos(90° - 1°) = cos 89°
• -cos(90° + 1°) = -cos 91°

Sin 1 Degrees Using Unit Circle

To find the value of sin 1 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 1° angle with the positive x-axis.
• The sin of 1 degrees equals the y-coordinate(0.0175) of the point of intersection (0.9998, 0.0175) of unit circle and r.

Hence the value of sin 1° = y = 0.0175 (approx)

☛ Also Check:

• sin 53 degrees
• sin 30 degrees
• sin 35 degrees
• sin 8 degrees
• sin 510 degrees
• sin 31 degrees

FAQs on Sin 1 Degrees

What is Sin 1 Degrees?

Sin 1 degrees is the value of sine trigonometric function for an angle equal to 1 degrees. The value of sin 1° is 0.0175 (approx).

How to Find the Value of Sin 1 Degrees?

The value of sin 1 degrees can be calculated by constructing an angle of 1° with the x-axis, and then finding the coordinates of the corresponding point (0.9998, 0.0175) on the unit circle. The value of sin 1° is equal to the y-coordinate (0.0175). ∴ sin 1° = 0.0175.

What is the Value of Sin 1° in Terms of Cosec 1°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 1° as 1/cosec(1°). The value of cosec 1° is equal to 57.29868.

What is the Value of Sin 1 Degrees in Terms of Cos 1°?

Using trigonometric identities, we can write sin 1° in terms of cos 1° as, sin(1°) = √(1-cos²(1°)). Here, the value of cos 1° is equal to 0.9998476.

How to Find Sin 1° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 1° can be given in terms of other trigonometric functions as:

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

☛ Also check: trigonometry table