Sin 28 Degrees

The value of sin 28 degrees is 0.4694715. . .. Sin 28 degrees in radians is written as sin (28° × π/180°), i.e., sin (7π/45) or sin (0.488692. . .). In this article, we will discuss the methods to find the value of sin 28 degrees with examples.

• Sin 28°: 0.4694715. . .
• Sin (-28 degrees): -0.4694715. . .
• Sin 28° in radians: sin (7π/45) or sin (0.4886921 . . .)

What is the Value of Sin 28 Degrees?

The value of sin 28 degrees in decimal is 0.469471562. . .. Sin 28 degrees can also be expressed using the equivalent of the given angle (28 degrees) in radians (0.48869 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 28 degrees = 28° × (π/180°) rad = 7π/45 or 0.4886 . . .
∴ sin 28° = sin(0.4886) = 0.4694715. . .

Explanation:

For sin 28 degrees, the angle 28° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 28° value = 0.4694715. . .
Since the sine function is a periodic function, we can represent sin 28° as, sin 28 degrees = sin(28° + n × 360°), n ∈ Z.
⇒ sin 28° = sin 388° = sin 748°, and so on.
Note: Since, sine is an odd function, the value of sin(-28°) = -sin(28°).

Methods to Find Value of Sin 28 Degrees

The sine function is positive in the 1st quadrant. The value of sin 28° is given as 0.46947. . .. We can find the value of sin 28 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 28 Degrees Using Unit Circle

To find the value of sin 28 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 28° angle with the positive x-axis.
• The sin of 28 degrees equals the y-coordinate(0.4695) of the point of intersection (0.8829, 0.4695) of unit circle and r.

Hence the value of sin 28° = y = 0.4695 (approx)

Sin 28° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 28 degrees as:

• ± √(1-cos²(28°))
• ± tan 28°/√(1 + tan²(28°))
• ± 1/√(1 + cot²(28°))
• ± √(sec²(28°) - 1)/sec 28°
• 1/cosec 28°

Note: Since 28° lies in the 1st Quadrant, the final value of sin 28° will be positive.

We can use trigonometric identities to represent sin 28° as,

• sin(180° - 28°) = sin 152°
• -sin(180° + 28°) = -sin 208°
• cos(90° - 28°) = cos 62°
• -cos(90° + 28°) = -cos 118°

☛ Also Check:

• sin 36 degrees
• sin 556 degrees
• sin 0 degrees
• sin 19 degrees
• sin 1000 degrees
• sin 85 degrees

FAQs on Sin 28 Degrees

What is Sin 28 Degrees?

Sin 28 degrees is the value of sine trigonometric function for an angle equal to 28 degrees. The value of sin 28° is 0.4695 (approx).

What is the Value of Sin 28 Degrees in Terms of Cot 28°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 28° can be written as 1/√(1 + cot²(28°)). Here, the value of cot 28° is equal to 1.88072.

How to Find Sin 28° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 28° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(28°))
• ± tan 28°/√(1 + tan²(28°))
• ± 1/√(1 + cot²(28°))
• ± √(sec²(28°) - 1)/sec 28°
• 1/cosec 28°

☛ Also check: trigonometric table

How to Find the Value of Sin 28 Degrees?

The value of sin 28 degrees can be calculated by constructing an angle of 28° with the x-axis, and then finding the coordinates of the corresponding point (0.8829, 0.4695) on the unit circle. The value of sin 28° is equal to the y-coordinate (0.4695). ∴ sin 28° = 0.4695.

What is the Value of Sin 28° in Terms of Sec 28°?

Since the sine function can be represented using the secant function, we can write sin 28° as √(sec²(28°) - 1)/sec 28°. The value of sec 28° is equal to 1.13257.