Sin 85 Degrees
The value of sin 85 degrees is 0.9961946. . .. Sin 85 degrees in radians is written as sin (85° × π/180°), i.e., sin (17π/36) or sin (1.483529. . .). In this article, we will discuss the methods to find the value of sin 85 degrees with examples.
 Sin 85°: 0.9961946. . .
 Sin (85 degrees): 0.9961946. . .
 Sin 85° in radians: sin (17π/36) or sin (1.4835298 . . .)
What is the Value of Sin 85 Degrees?
The value of sin 85 degrees in decimal is 0.996194698. . .. Sin 85 degrees can also be expressed using the equivalent of the given angle (85 degrees) in radians (1.48352 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 85 degrees = 85° × (π/180°) rad = 17π/36 or 1.4835 . . .
∴ sin 85° = sin(1.4835) = 0.9961946. . .
Explanation:
For sin 85 degrees, the angle 85° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 85° value = 0.9961946. . .
Since the sine function is a periodic function, we can represent sin 85° as, sin 85 degrees = sin(85° + n × 360°), n ∈ Z.
⇒ sin 85° = sin 445° = sin 805°, and so on.
Note: Since, sine is an odd function, the value of sin(85°) = sin(85°).
Methods to Find Value of Sin 85 Degrees
The sine function is positive in the 1st quadrant. The value of sin 85° is given as 0.99619. . .. We can find the value of sin 85 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Sin 85° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 85 degrees as:
 ± √(1cos²(85°))
 ± tan 85°/√(1 + tan²(85°))
 ± 1/√(1 + cot²(85°))
 ± √(sec²(85°)  1)/sec 85°
 1/cosec 85°
Note: Since 85° lies in the 1st Quadrant, the final value of sin 85° will be positive.
We can use trigonometric identities to represent sin 85° as,
 sin(180°  85°) = sin 95°
 sin(180° + 85°) = sin 265°
 cos(90°  85°) = cos 5°
 cos(90° + 85°) = cos 175°
Sin 85 Degrees Using Unit Circle
To find the value of sin 85 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 85° angle with the positive xaxis.
 The sin of 85 degrees equals the ycoordinate(0.9962) of the point of intersection (0.0872, 0.9962) of unit circle and r.
Hence the value of sin 85° = y = 0.9962 (approx)
☛ Also Check:
Examples Using Sin 85 Degrees

Example 1: Using the value of sin 85°, solve: (1cos²(85°)).
Solution:
We know, (1cos²(85°)) = (sin²(85°)) = 0.9924
⇒ (1cos²(85°)) = 0.9924 
Example 2: Find the value of sin 85° if cosec 85° is 1.0038.
Solution:
Since, sin 85° = 1/csc 85°
⇒ sin 85° = 1/1.0038 = 0.9962 
Example 3: Find the value of 2 × (sin 42.5° cos 42.5°). [Hint: Use sin 85° = 0.9962]
Solution:
Using the sin 2a formula,
2 sin 42.5° cos 42.5° = sin(2 × 42.5°) = sin 85°
∵ sin 85° = 0.9962
⇒ 2 × (sin 42.5° cos 42.5°) = 0.9962
FAQs on Sin 85 Degrees
What is Sin 85 Degrees?
Sin 85 degrees is the value of sine trigonometric function for an angle equal to 85 degrees. The value of sin 85° is 0.9962 (approx).
What is the Value of Sin 85° in Terms of Cosec 85°?
Since the cosecant function is the reciprocal of the sine function, we can write sin 85° as 1/cosec(85°). The value of cosec 85° is equal to 1.00381.
What is the Value of Sin 85 Degrees in Terms of Tan 85°?
We know, using trig identities, we can write sin 85° as tan 85°/√(1 + tan²(85°)). Here, the value of tan 85° is equal to 11.430052.
How to Find the Value of Sin 85 Degrees?
The value of sin 85 degrees can be calculated by constructing an angle of 85° with the xaxis, and then finding the coordinates of the corresponding point (0.0872, 0.9962) on the unit circle. The value of sin 85° is equal to the ycoordinate (0.9962). ∴ sin 85° = 0.9962.
How to Find Sin 85° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 85° can be given in terms of other trigonometric functions as:
 ± √(1cos²(85°))
 ± tan 85°/√(1 + tan²(85°))
 ± 1/√(1 + cot²(85°))
 ± √(sec²(85°)  1)/sec 85°
 1/cosec 85°
☛ Also check: trigonometric table
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