Sin 23 Degrees

The value of sin 23 degrees is 0.3907311. . .. Sin 23 degrees in radians is written as sin (23° × π/180°), i.e., sin (0.401425. . .). In this article, we will discuss the methods to find the value of sin 23 degrees with examples.

• Sin 23°: 0.3907311. . .
• Sin (-23 degrees): -0.3907311. . .
• Sin 23° in radians: sin (0.4014257 . . .)

What is the Value of Sin 23 Degrees?

The value of sin 23 degrees in decimal is 0.390731128. . .. Sin 23 degrees can also be expressed using the equivalent of the given angle (23 degrees) in radians (0.40142 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 23 degrees = 23° × (π/180°) rad = 0.4014 . . .
∴ sin 23° = sin(0.4014) = 0.3907311. . .

Explanation:

For sin 23 degrees, the angle 23° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 23° value = 0.3907311. . .
Since the sine function is a periodic function, we can represent sin 23° as, sin 23 degrees = sin(23° + n × 360°), n ∈ Z.
⇒ sin 23° = sin 383° = sin 743°, and so on.
Note: Since, sine is an odd function, the value of sin(-23°) = -sin(23°).

Methods to Find Value of Sin 23 Degrees

The sine function is positive in the 1st quadrant. The value of sin 23° is given as 0.39073. . .. We can find the value of sin 23 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 23° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 23 degrees as:

• ± √(1-cos²(23°))
• ± tan 23°/√(1 + tan²(23°))
• ± 1/√(1 + cot²(23°))
• ± √(sec²(23°) - 1)/sec 23°
• 1/cosec 23°

Note: Since 23° lies in the 1st Quadrant, the final value of sin 23° will be positive.

We can use trigonometric identities to represent sin 23° as,

• sin(180° - 23°) = sin 157°
• -sin(180° + 23°) = -sin 203°
• cos(90° - 23°) = cos 67°
• -cos(90° + 23°) = -cos 113°

Sin 23 Degrees Using Unit Circle

To find the value of sin 23 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 23° angle with the positive x-axis.
• The sin of 23 degrees equals the y-coordinate(0.3907) of the point of intersection (0.9205, 0.3907) of unit circle and r.

Hence the value of sin 23° = y = 0.3907 (approx)

☛ Also Check:

• sin 37 degrees
• sin 18 degrees
• sin 36 degrees
• sin 21 degrees
• sin 80 degrees
• sin 405 degrees

FAQs on Sin 23 Degrees

What is Sin 23 Degrees?

Sin 23 degrees is the value of sine trigonometric function for an angle equal to 23 degrees. The value of sin 23° is 0.3907 (approx).

How to Find Sin 23° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 23° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(23°))
• ± tan 23°/√(1 + tan²(23°))
• ± 1/√(1 + cot²(23°))
• ± √(sec²(23°) - 1)/sec 23°
• 1/cosec 23°

☛ Also check: trigonometric table

What is the Value of Sin 23° in Terms of Sec 23°?

Since the sine function can be represented using the secant function, we can write sin 23° as √(sec²(23°) - 1)/sec 23°. The value of sec 23° is equal to 1.08636.

How to Find the Value of Sin 23 Degrees?

The value of sin 23 degrees can be calculated by constructing an angle of 23° with the x-axis, and then finding the coordinates of the corresponding point (0.9205, 0.3907) on the unit circle. The value of sin 23° is equal to the y-coordinate (0.3907). ∴ sin 23° = 0.3907.

What is the Value of Sin 23 Degrees in Terms of Cos 23°?

Using trigonometric identities, we can write sin 23° in terms of cos 23° as, sin(23°) = √(1-cos²(23°)). Here, the value of cos 23° is equal to 0.9205048.