Sin 21 Degrees

The value of sin 21 degrees is 0.3583679. . .. Sin 21 degrees in radians is written as sin (21° × π/180°), i.e., sin (7π/60) or sin (0.366519. . .). In this article, we will discuss the methods to find the value of sin 21 degrees with examples.

• Sin 21°: 0.3583679. . .
• Sin (-21 degrees): -0.3583679. . .
• Sin 21° in radians: sin (7π/60) or sin (0.3665191 . . .)

What is the Value of Sin 21 Degrees?

The value of sin 21 degrees in decimal is 0.358367949. . .. Sin 21 degrees can also be expressed using the equivalent of the given angle (21 degrees) in radians (0.36651 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 21 degrees = 21° × (π/180°) rad = 7π/60 or 0.3665 . . .
∴ sin 21° = sin(0.3665) = 0.3583679. . .

Explanation:

For sin 21 degrees, the angle 21° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 21° value = 0.3583679. . .
Since the sine function is a periodic function, we can represent sin 21° as, sin 21 degrees = sin(21° + n × 360°), n ∈ Z.
⇒ sin 21° = sin 381° = sin 741°, and so on.
Note: Since, sine is an odd function, the value of sin(-21°) = -sin(21°).

Methods to Find Value of Sin 21 Degrees

The sine function is positive in the 1st quadrant. The value of sin 21° is given as 0.35836. . .. We can find the value of sin 21 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 21 Degrees Using Unit Circle

To find the value of sin 21 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 21° angle with the positive x-axis.
• The sin of 21 degrees equals the y-coordinate(0.3584) of the point of intersection (0.9336, 0.3584) of unit circle and r.

Hence the value of sin 21° = y = 0.3584 (approx)

Sin 21° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 21 degrees as:

• ± √(1-cos²(21°))
• ± tan 21°/√(1 + tan²(21°))
• ± 1/√(1 + cot²(21°))
• ± √(sec²(21°) - 1)/sec 21°
• 1/cosec 21°

Note: Since 21° lies in the 1st Quadrant, the final value of sin 21° will be positive.

We can use trigonometric identities to represent sin 21° as,

• sin(180° - 21°) = sin 159°
• -sin(180° + 21°) = -sin 201°
• cos(90° - 21°) = cos 69°
• -cos(90° + 21°) = -cos 111°

☛ Also Check:

• sin 270 degrees
• sin 36 degrees
• sin 150 degrees
• sin 57 degrees
• sin 71 degrees
• sin 158 degrees

FAQs on Sin 21 Degrees

What is Sin 21 Degrees?

Sin 21 degrees is the value of sine trigonometric function for an angle equal to 21 degrees. The value of sin 21° is 0.3584 (approx).

How to Find Sin 21° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 21° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(21°))
• ± tan 21°/√(1 + tan²(21°))
• ± 1/√(1 + cot²(21°))
• ± √(sec²(21°) - 1)/sec 21°
• 1/cosec 21°

☛ Also check: trigonometric table

What is the Exact Value of sin 21 Degrees?

The exact value of sin 21 degrees can be given accurately up to 8 decimal places as 0.35836794.

What is the Value of Sin 21 Degrees in Terms of Cos 21°?

Using trigonometric identities, we can write sin 21° in terms of cos 21° as, sin(21°) = √(1-cos²(21°)). Here, the value of cos 21° is equal to 0.9335804.

How to Find the Value of Sin 21 Degrees?

The value of sin 21 degrees can be calculated by constructing an angle of 21° with the x-axis, and then finding the coordinates of the corresponding point (0.9336, 0.3584) on the unit circle. The value of sin 21° is equal to the y-coordinate (0.3584). ∴ sin 21° = 0.3584.