Sin 3 Degrees

The value of sin 3 degrees is 0.0523359. . .. Sin 3 degrees in radians is written as sin (3° × π/180°), i.e., sin (π/60) or sin (0.052359. . .). In this article, we will discuss the methods to find the value of sin 3 degrees with examples.

• Sin 3°: 0.0523359. . .
• Sin (-3 degrees): -0.0523359. . .
• Sin 3° in radians: sin (π/60) or sin (0.0523598 . . .)

What is the Value of Sin 3 Degrees?

The value of sin 3 degrees in decimal is 0.052335956. . .. Sin 3 degrees can also be expressed using the equivalent of the given angle (3 degrees) in radians (0.05235 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 3 degrees = 3° × (π/180°) rad = π/60 or 0.0523 . . .
∴ sin 3° = sin(0.0523) = 0.0523359. . .

Explanation:

For sin 3 degrees, the angle 3° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 3° value = 0.0523359. . .
Since the sine function is a periodic function, we can represent sin 3° as, sin 3 degrees = sin(3° + n × 360°), n ∈ Z.
⇒ sin 3° = sin 363° = sin 723°, and so on.
Note: Since, sine is an odd function, the value of sin(-3°) = -sin(3°).

Methods to Find Value of Sin 3 Degrees

The sine function is positive in the 1st quadrant. The value of sin 3° is given as 0.05233. . .. We can find the value of sin 3 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 3 Degrees Using Unit Circle

To find the value of sin 3 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 3° angle with the positive x-axis.
• The sin of 3 degrees equals the y-coordinate(0.0523) of the point of intersection (0.9986, 0.0523) of unit circle and r.

Hence the value of sin 3° = y = 0.0523 (approx)

Sin 3° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 3 degrees as:

• ± √(1-cos²(3°))
• ± tan 3°/√(1 + tan²(3°))
• ± 1/√(1 + cot²(3°))
• ± √(sec²(3°) - 1)/sec 3°
• 1/cosec 3°

Note: Since 3° lies in the 1st Quadrant, the final value of sin 3° will be positive.

We can use trigonometric identities to represent sin 3° as,

• sin(180° - 3°) = sin 177°
• -sin(180° + 3°) = -sin 183°
• cos(90° - 3°) = cos 87°
• -cos(90° + 3°) = -cos 93°

☛ Also Check:

• sin 45 degrees
• sin 15 degrees
• sin 556 degrees
• sin 67 degrees
• sin 255 degrees
• sin 170 degrees

FAQs on Sin 3 Degrees

What is Sin 3 Degrees?

Sin 3 degrees is the value of sine trigonometric function for an angle equal to 3 degrees. The value of sin 3° is 0.0523 (approx).

How to Find the Value of Sin 3 Degrees?

The value of sin 3 degrees can be calculated by constructing an angle of 3° with the x-axis, and then finding the coordinates of the corresponding point (0.9986, 0.0523) on the unit circle. The value of sin 3° is equal to the y-coordinate (0.0523). ∴ sin 3° = 0.0523.

How to Find Sin 3° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 3° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(3°))
• ± tan 3°/√(1 + tan²(3°))
• ± 1/√(1 + cot²(3°))
• ± √(sec²(3°) - 1)/sec 3°
• 1/cosec 3°

☛ Also check: trigonometry table

What is the Value of Sin 3 Degrees in Terms of Tan 3°?

We know, using trig identities, we can write sin 3° as tan 3°/√(1 + tan²(3°)). Here, the value of tan 3° is equal to 0.052407.

What is the Exact Value of sin 3 Degrees?

The exact value of sin 3 degrees can be given accurately up to 8 decimal places as 0.05233595.