Sin 24 Degrees

The value of sin 24 degrees is 0.4067366. . .. Sin 24 degrees in radians is written as sin (24° × π/180°), i.e., sin (2π/15) or sin (0.418879. . .). In this article, we will discuss the methods to find the value of sin 24 degrees with examples.

• Sin 24°: 0.4067366. . .
• Sin (-24 degrees): -0.4067366. . .
• Sin 24° in radians: sin (2π/15) or sin (0.4188790 . . .)

What is the Value of Sin 24 Degrees?

The value of sin 24 degrees in decimal is 0.406736643. . .. Sin 24 degrees can also be expressed using the equivalent of the given angle (24 degrees) in radians (0.41887 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 24 degrees = 24° × (π/180°) rad = 2π/15 or 0.4188 . . .
∴ sin 24° = sin(0.4188) = 0.4067366. . .

Explanation:

For sin 24 degrees, the angle 24° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 24° value = 0.4067366. . .
Since the sine function is a periodic function, we can represent sin 24° as, sin 24 degrees = sin(24° + n × 360°), n ∈ Z.
⇒ sin 24° = sin 384° = sin 744°, and so on.
Note: Since, sine is an odd function, the value of sin(-24°) = -sin(24°).

Methods to Find Value of Sin 24 Degrees

The sine function is positive in the 1st quadrant. The value of sin 24° is given as 0.40673. . .. We can find the value of sin 24 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 24° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 24 degrees as:

• ± √(1-cos²(24°))
• ± tan 24°/√(1 + tan²(24°))
• ± 1/√(1 + cot²(24°))
• ± √(sec²(24°) - 1)/sec 24°
• 1/cosec 24°

Note: Since 24° lies in the 1st Quadrant, the final value of sin 24° will be positive.

We can use trigonometric identities to represent sin 24° as,

• sin(180° - 24°) = sin 156°
• -sin(180° + 24°) = -sin 204°
• cos(90° - 24°) = cos 66°
• -cos(90° + 24°) = -cos 114°

Sin 24 Degrees Using Unit Circle

To find the value of sin 24 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 24° angle with the positive x-axis.
• The sin of 24 degrees equals the y-coordinate(0.4067) of the point of intersection (0.9135, 0.4067) of unit circle and r.

Hence the value of sin 24° = y = 0.4067 (approx)

☛ Also Check:

• sin 1 degrees
• sin 120 degrees
• sin 10 degrees
• sin 165 degrees
• sin 345 degrees
• sin 330 degrees

FAQs on Sin 24 Degrees

What is Sin 24 Degrees?

Sin 24 degrees is the value of sine trigonometric function for an angle equal to 24 degrees. The value of sin 24° is 0.4067 (approx).

What is the Value of Sin 24 Degrees in Terms of Cot 24°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 24° can be written as 1/√(1 + cot²(24°)). Here, the value of cot 24° is equal to 2.24603.

What is the Exact Value of sin 24 Degrees?

The exact value of sin 24 degrees can be given accurately up to 8 decimal places as 0.40673664.

How to Find the Value of Sin 24 Degrees?

The value of sin 24 degrees can be calculated by constructing an angle of 24° with the x-axis, and then finding the coordinates of the corresponding point (0.9135, 0.4067) on the unit circle. The value of sin 24° is equal to the y-coordinate (0.4067). ∴ sin 24° = 0.4067.

How to Find Sin 24° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 24° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(24°))
• ± tan 24°/√(1 + tan²(24°))
• ± 1/√(1 + cot²(24°))
• ± √(sec²(24°) - 1)/sec 24°
• 1/cosec 24°

☛ Also check: trigonometry table