Sin 4 Degrees

The value of sin 4 degrees is 0.0697564. . .. Sin 4 degrees in radians is written as sin (4° × π/180°), i.e., sin (π/45) or sin (0.069813. . .). In this article, we will discuss the methods to find the value of sin 4 degrees with examples.

• Sin 4°: 0.0697564. . .
• Sin (-4 degrees): -0.0697564. . .
• Sin 4° in radians: sin (π/45) or sin (0.0698131 . . .)

What is the Value of Sin 4 Degrees?

The value of sin 4 degrees in decimal is 0.069756473. . .. Sin 4 degrees can also be expressed using the equivalent of the given angle (4 degrees) in radians (0.06981 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 4 degrees = 4° × (π/180°) rad = π/45 or 0.0698 . . .
∴ sin 4° = sin(0.0698) = 0.0697564. . .

Explanation:

For sin 4 degrees, the angle 4° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 4° value = 0.0697564. . .
Since the sine function is a periodic function, we can represent sin 4° as, sin 4 degrees = sin(4° + n × 360°), n ∈ Z.
⇒ sin 4° = sin 364° = sin 724°, and so on.
Note: Since, sine is an odd function, the value of sin(-4°) = -sin(4°).

Methods to Find Value of Sin 4 Degrees

The sine function is positive in the 1st quadrant. The value of sin 4° is given as 0.06975. . .. We can find the value of sin 4 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 4 Degrees Using Unit Circle

To find the value of sin 4 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 4° angle with the positive x-axis.
• The sin of 4 degrees equals the y-coordinate(0.0698) of the point of intersection (0.9976, 0.0698) of unit circle and r.

Hence the value of sin 4° = y = 0.0698 (approx)

Sin 4° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 4 degrees as:

• ± √(1-cos²(4°))
• ± tan 4°/√(1 + tan²(4°))
• ± 1/√(1 + cot²(4°))
• ± √(sec²(4°) - 1)/sec 4°
• 1/cosec 4°

Note: Since 4° lies in the 1st Quadrant, the final value of sin 4° will be positive.

We can use trigonometric identities to represent sin 4° as,

• sin(180° - 4°) = sin 176°
• -sin(180° + 4°) = -sin 184°
• cos(90° - 4°) = cos 86°
• -cos(90° + 4°) = -cos 94°

☛ Also Check:

• sin 0 degrees
• sin 20 degrees
• sin 45 degrees
• sin 690 degrees
• sin 39 degrees
• sin 857 degrees

FAQs on Sin 4 Degrees

What is Sin 4 Degrees?

Sin 4 degrees is the value of sine trigonometric function for an angle equal to 4 degrees. The value of sin 4° is 0.0698 (approx).

How to Find the Value of Sin 4 Degrees?

The value of sin 4 degrees can be calculated by constructing an angle of 4° with the x-axis, and then finding the coordinates of the corresponding point (0.9976, 0.0698) on the unit circle. The value of sin 4° is equal to the y-coordinate (0.0698). ∴ sin 4° = 0.0698.

What is the Value of Sin 4 Degrees in Terms of Cot 4°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 4° can be written as 1/√(1 + cot²(4°)). Here, the value of cot 4° is equal to 14.30066.

How to Find Sin 4° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 4° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(4°))
• ± tan 4°/√(1 + tan²(4°))
• ± 1/√(1 + cot²(4°))
• ± √(sec²(4°) - 1)/sec 4°
• 1/cosec 4°

☛ Also check: trigonometric table

What is the Exact Value of sin 4 Degrees?

The exact value of sin 4 degrees can be given accurately up to 8 decimal places as 0.06975647.