Sin 9 Degrees

The value of sin 9 degrees is 0.1564344. . .. Sin 9 degrees in radians is written as sin (9° × π/180°), i.e., sin (π/20) or sin (0.157079. . .). In this article, we will discuss the methods to find the value of sin 9 degrees with examples.

• Sin 9°: 0.1564344. . .
• Sin (-9 degrees): -0.1564344. . .
• Sin 9° in radians: sin (π/20) or sin (0.1570796 . . .)

What is the Value of Sin 9 Degrees?

The value of sin 9 degrees in decimal is 0.156434465. . .. Sin 9 degrees can also be expressed using the equivalent of the given angle (9 degrees) in radians (0.15707 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 9 degrees = 9° × (π/180°) rad = π/20 or 0.1570 . . .
∴ sin 9° = sin(0.1570) = 0.1564344. . .

Explanation:

For sin 9 degrees, the angle 9° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 9° value = 0.1564344. . .
Since the sine function is a periodic function, we can represent sin 9° as, sin 9 degrees = sin(9° + n × 360°), n ∈ Z.
⇒ sin 9° = sin 369° = sin 729°, and so on.
Note: Since, sine is an odd function, the value of sin(-9°) = -sin(9°).

Methods to Find Value of Sin 9 Degrees

The sine function is positive in the 1st quadrant. The value of sin 9° is given as 0.15643. . .. We can find the value of sin 9 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 9 Degrees Using Unit Circle

To find the value of sin 9 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 9° angle with the positive x-axis.
• The sin of 9 degrees equals the y-coordinate(0.1564) of the point of intersection (0.9877, 0.1564) of unit circle and r.

Hence the value of sin 9° = y = 0.1564 (approx)

Sin 9° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 9 degrees as:

• ± √(1-cos²(9°))
• ± tan 9°/√(1 + tan²(9°))
• ± 1/√(1 + cot²(9°))
• ± √(sec²(9°) - 1)/sec 9°
• 1/cosec 9°

Note: Since 9° lies in the 1st Quadrant, the final value of sin 9° will be positive.

We can use trigonometric identities to represent sin 9° as,

• sin(180° - 9°) = sin 171°
• -sin(180° + 9°) = -sin 189°
• cos(90° - 9°) = cos 81°
• -cos(90° + 9°) = -cos 99°

☛ Also Check:

• sin 30 degrees
• sin 11 degrees
• sin 104 degrees
• sin 16 degrees
• sin 99 degrees
• sin 390 degrees

FAQs on Sin 9 Degrees

What is Sin 9 Degrees?

Sin 9 degrees is the value of sine trigonometric function for an angle equal to 9 degrees. The value of sin 9° is 0.1564 (approx).

What is the Value of Sin 9° in Terms of Sec 9°?

Since the sine function can be represented using the secant function, we can write sin 9° as √(sec²(9°) - 1)/sec 9°. The value of sec 9° is equal to 1.012465.

What is the Value of Sin 9 Degrees in Terms of Tan 9°?

We know, using trig identities, we can write sin 9° as tan 9°/√(1 + tan²(9°)). Here, the value of tan 9° is equal to 0.158384.

How to Find Sin 9° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 9° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(9°))
• ± tan 9°/√(1 + tan²(9°))
• ± 1/√(1 + cot²(9°))
• ± √(sec²(9°) - 1)/sec 9°
• 1/cosec 9°

☛ Also check: trigonometric table

How to Find the Value of Sin 9 Degrees?

The value of sin 9 degrees can be calculated by constructing an angle of 9° with the x-axis, and then finding the coordinates of the corresponding point (0.9877, 0.1564) on the unit circle. The value of sin 9° is equal to the y-coordinate (0.1564). ∴ sin 9° = 0.1564.