Sin 20 Degrees

The value of sin 20 degrees is 0.3420201. . .. Sin 20 degrees in radians is written as sin (20° × π/180°), i.e., sin (π/9) or sin (0.349065. . .). In this article, we will discuss the methods to find the value of sin 20 degrees with examples.

• Sin 20°: 0.3420201. . .
• Sin (-20 degrees): -0.3420201. . .
• Sin 20° in radians: sin (π/9) or sin (0.3490658 . . .)

What is the Value of Sin 20 Degrees?

The value of sin 20 degrees in decimal is 0.342020143. . .. Sin 20 degrees can also be expressed using the equivalent of the given angle (20 degrees) in radians (0.34906 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 20 degrees = 20° × (π/180°) rad = π/9 or 0.3490 . . .
∴ sin 20° = sin(0.3490) = 0.3420201. . .

Explanation:

For sin 20 degrees, the angle 20° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 20° value = 0.3420201. . .
Since the sine function is a periodic function, we can represent sin 20° as, sin 20 degrees = sin(20° + n × 360°), n ∈ Z.
⇒ sin 20° = sin 380° = sin 740°, and so on.
Note: Since, sine is an odd function, the value of sin(-20°) = -sin(20°).

Methods to Find Value of Sin 20 Degrees

The sine function is positive in the 1st quadrant. The value of sin 20° is given as 0.34202. . .. We can find the value of sin 20 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 20 Degrees Using Unit Circle

To find the value of sin 20 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 20° angle with the positive x-axis.
• The sin of 20 degrees equals the y-coordinate(0.342) of the point of intersection (0.9397, 0.342) of unit circle and r.

Hence the value of sin 20° = y = 0.342 (approx)

Sin 20° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 20 degrees as:

• ± √(1-cos²(20°))
• ± tan 20°/√(1 + tan²(20°))
• ± 1/√(1 + cot²(20°))
• ± √(sec²(20°) - 1)/sec 20°
• 1/cosec 20°

Note: Since 20° lies in the 1st Quadrant, the final value of sin 20° will be positive.

We can use trigonometric identities to represent sin 20° as,

• sin(180° - 20°) = sin 160°
• -sin(180° + 20°) = -sin 200°
• cos(90° - 20°) = cos 70°
• -cos(90° + 20°) = -cos 110°

☛ Also Check:

• sin 3 degrees
• sin 90 degrees
• sin 75 degrees
• sin 28 degrees
• sin 9 degrees
• sin 17 degrees

FAQs on Sin 20 Degrees

What is Sin 20 Degrees?

Sin 20 degrees is the value of sine trigonometric function for an angle equal to 20 degrees. The value of sin 20° is 0.342 (approx).

What is the Value of Sin 20° in Terms of Sec 20°?

Since the sine function can be represented using the secant function, we can write sin 20° as √(sec²(20°) - 1)/sec 20°. The value of sec 20° is equal to 1.064178.

How to Find Sin 20° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 20° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(20°))
• ± tan 20°/√(1 + tan²(20°))
• ± 1/√(1 + cot²(20°))
• ± √(sec²(20°) - 1)/sec 20°
• 1/cosec 20°

☛ Also check: trigonometric table

How to Find the Value of Sin 20 Degrees?

The value of sin 20 degrees can be calculated by constructing an angle of 20° with the x-axis, and then finding the coordinates of the corresponding point (0.9397, 0.342) on the unit circle. The value of sin 20° is equal to the y-coordinate (0.342). ∴ sin 20° = 0.342.

What is the Value of Sin 20 Degrees in Terms of Tan 20°?

We know, using trig identities, we can write sin 20° as tan 20°/√(1 + tan²(20°)). Here, the value of tan 20° is equal to 0.363970.