Sin 83 Degrees

The value of sin 83 degrees is 0.9925461. . .. Sin 83 degrees in radians is written as sin (83° × π/180°), i.e., sin (1.448623. . .). In this article, we will discuss the methods to find the value of sin 83 degrees with examples.

• Sin 83°: 0.9925461. . .
• Sin (-83 degrees): -0.9925461. . .
• Sin 83° in radians: sin (1.4486232 . . .)

What is the Value of Sin 83 Degrees?

The value of sin 83 degrees in decimal is 0.992546151. . .. Sin 83 degrees can also be expressed using the equivalent of the given angle (83 degrees) in radians (1.44862 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 83 degrees = 83° × (π/180°) rad = 1.4486 . . .
∴ sin 83° = sin(1.4486) = 0.9925461. . .

Explanation:

For sin 83 degrees, the angle 83° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 83° value = 0.9925461. . .
Since the sine function is a periodic function, we can represent sin 83° as, sin 83 degrees = sin(83° + n × 360°), n ∈ Z.
⇒ sin 83° = sin 443° = sin 803°, and so on.
Note: Since, sine is an odd function, the value of sin(-83°) = -sin(83°).

Methods to Find Value of Sin 83 Degrees

The sine function is positive in the 1st quadrant. The value of sin 83° is given as 0.99254. . .. We can find the value of sin 83 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 83° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 83 degrees as:

• ± √(1-cos²(83°))
• ± tan 83°/√(1 + tan²(83°))
• ± 1/√(1 + cot²(83°))
• ± √(sec²(83°) - 1)/sec 83°
• 1/cosec 83°

Note: Since 83° lies in the 1st Quadrant, the final value of sin 83° will be positive.

We can use trigonometric identities to represent sin 83° as,

• sin(180° - 83°) = sin 97°
• -sin(180° + 83°) = -sin 263°
• cos(90° - 83°) = cos 7°
• -cos(90° + 83°) = -cos 173°

Sin 83 Degrees Using Unit Circle

To find the value of sin 83 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 83° angle with the positive x-axis.
• The sin of 83 degrees equals the y-coordinate(0.9925) of the point of intersection (0.1219, 0.9925) of unit circle and r.

Hence the value of sin 83° = y = 0.9925 (approx)

☛ Also Check:

• sin 36 degrees
• sin 180 degrees
• sin 2 degrees
• sin 170 degrees
• sin 108 degrees
• sin 56 degrees

FAQs on Sin 83 Degrees

What is Sin 83 Degrees?

Sin 83 degrees is the value of sine trigonometric function for an angle equal to 83 degrees. The value of sin 83° is 0.9925 (approx).

What is the Value of Sin 83 Degrees in Terms of Cos 83°?

Using trigonometric identities, we can write sin 83° in terms of cos 83° as, sin(83°) = √(1-cos²(83°)). Here, the value of cos 83° is equal to 0.1218693.

How to Find the Value of Sin 83 Degrees?

The value of sin 83 degrees can be calculated by constructing an angle of 83° with the x-axis, and then finding the coordinates of the corresponding point (0.1219, 0.9925) on the unit circle. The value of sin 83° is equal to the y-coordinate (0.9925). ∴ sin 83° = 0.9925.

What is the Exact Value of sin 83 Degrees?

The exact value of sin 83 degrees can be given accurately up to 8 decimal places as 0.99254615.

How to Find Sin 83° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 83° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(83°))
• ± tan 83°/√(1 + tan²(83°))
• ± 1/√(1 + cot²(83°))
• ± √(sec²(83°) - 1)/sec 83°
• 1/cosec 83°

☛ Also check: trigonometric table