Sin 80 Degrees

The value of sin 80 degrees is 0.9848077. . .. Sin 80 degrees in radians is written as sin (80° × π/180°), i.e., sin (4π/9) or sin (1.396263. . .). In this article, we will discuss the methods to find the value of sin 80 degrees with examples.

• Sin 80°: 0.9848077. . .
• Sin (-80 degrees): -0.9848077. . .
• Sin 80° in radians: sin (4π/9) or sin (1.3962634 . . .)

What is the Value of Sin 80 Degrees?

The value of sin 80 degrees in decimal is 0.984807753. . .. Sin 80 degrees can also be expressed using the equivalent of the given angle (80 degrees) in radians (1.39626 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 80 degrees = 80° × (π/180°) rad = 4π/9 or 1.3962 . . .
∴ sin 80° = sin(1.3962) = 0.9848077. . .

Explanation:

For sin 80 degrees, the angle 80° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 80° value = 0.9848077. . .
Since the sine function is a periodic function, we can represent sin 80° as, sin 80 degrees = sin(80° + n × 360°), n ∈ Z.
⇒ sin 80° = sin 440° = sin 800°, and so on.
Note: Since, sine is an odd function, the value of sin(-80°) = -sin(80°).

Methods to Find Value of Sin 80 Degrees

The sine function is positive in the 1st quadrant. The value of sin 80° is given as 0.98480. . .. We can find the value of sin 80 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 80 Degrees Using Unit Circle

To find the value of sin 80 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 80° angle with the positive x-axis.
• The sin of 80 degrees equals the y-coordinate(0.9848) of the point of intersection (0.1736, 0.9848) of unit circle and r.

Hence the value of sin 80° = y = 0.9848 (approx)

Sin 80° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 80 degrees as:

• ± √(1-cos²(80°))
• ± tan 80°/√(1 + tan²(80°))
• ± 1/√(1 + cot²(80°))
• ± √(sec²(80°) - 1)/sec 80°
• 1/cosec 80°

Note: Since 80° lies in the 1st Quadrant, the final value of sin 80° will be positive.

We can use trigonometric identities to represent sin 80° as,

• sin(180° - 80°) = sin 100°
• -sin(180° + 80°) = -sin 260°
• cos(90° - 80°) = cos 10°
• -cos(90° + 80°) = -cos 170°

☛ Also Check:

• sin 20 degrees
• sin 13 degrees
• sin 270 degrees
• sin 31 degrees
• sin 46 degrees
• sin 110 degrees

FAQs on Sin 80 Degrees

What is Sin 80 Degrees?

Sin 80 degrees is the value of sine trigonometric function for an angle equal to 80 degrees. The value of sin 80° is 0.9848 (approx).

How to Find Sin 80° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 80° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(80°))
• ± tan 80°/√(1 + tan²(80°))
• ± 1/√(1 + cot²(80°))
• ± √(sec²(80°) - 1)/sec 80°
• 1/cosec 80°

☛ Also check: trigonometric table

How to Find the Value of Sin 80 Degrees?

The value of sin 80 degrees can be calculated by constructing an angle of 80° with the x-axis, and then finding the coordinates of the corresponding point (0.1736, 0.9848) on the unit circle. The value of sin 80° is equal to the y-coordinate (0.9848). ∴ sin 80° = 0.9848.

What is the Value of Sin 80 Degrees in Terms of Cos 80°?

Using trigonometric identities, we can write sin 80° in terms of cos 80° as, sin(80°) = √(1-cos²(80°)). Here, the value of cos 80° is equal to 0.1736481.

What is the Exact Value of sin 80 Degrees?

The exact value of sin 80 degrees can be given accurately up to 8 decimal places as 0.98480775.