Sin 89 Degrees
The value of sin 89 degrees is 0.9998476. . .. Sin 89 degrees in radians is written as sin (89° × π/180°), i.e., sin (1.553343. . .). In this article, we will discuss the methods to find the value of sin 89 degrees with examples.
 Sin 89°: 0.9998476. . .
 Sin (89 degrees): 0.9998476. . .
 Sin 89° in radians: sin (1.5533430 . . .)
What is the Value of Sin 89 Degrees?
The value of sin 89 degrees in decimal is 0.999847695. . .. Sin 89 degrees can also be expressed using the equivalent of the given angle (89 degrees) in radians (1.55334 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 89 degrees = 89° × (π/180°) rad = 1.5533 . . .
∴ sin 89° = sin(1.5533) = 0.9998476. . .
Explanation:
For sin 89 degrees, the angle 89° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 89° value = 0.9998476. . .
Since the sine function is a periodic function, we can represent sin 89° as, sin 89 degrees = sin(89° + n × 360°), n ∈ Z.
⇒ sin 89° = sin 449° = sin 809°, and so on.
Note: Since, sine is an odd function, the value of sin(89°) = sin(89°).
Methods to Find Value of Sin 89 Degrees
The sine function is positive in the 1st quadrant. The value of sin 89° is given as 0.99984. . .. We can find the value of sin 89 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Sin 89° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 89 degrees as:
 ± √(1cos²(89°))
 ± tan 89°/√(1 + tan²(89°))
 ± 1/√(1 + cot²(89°))
 ± √(sec²(89°)  1)/sec 89°
 1/cosec 89°
Note: Since 89° lies in the 1st Quadrant, the final value of sin 89° will be positive.
We can use trigonometric identities to represent sin 89° as,
 sin(180°  89°) = sin 91°
 sin(180° + 89°) = sin 269°
 cos(90°  89°) = cos 1°
 cos(90° + 89°) = cos 179°
Sin 89 Degrees Using Unit Circle
To find the value of sin 89 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 89° angle with the positive xaxis.
 The sin of 89 degrees equals the ycoordinate(0.9998) of the point of intersection (0.0175, 0.9998) of unit circle and r.
Hence the value of sin 89° = y = 0.9998 (approx)
☛ Also Check:
Examples Using Sin 89 Degrees

Example 1: Using the value of sin 89°, solve: (1cos²(89°)).
Solution:
We know, (1cos²(89°)) = (sin²(89°)) = 0.9997
⇒ (1cos²(89°)) = 0.9997 
Example 2: Simplify: 2 (sin 89°/sin 449°)
Solution:
We know sin 89° = sin 449°
⇒ 2 sin 89°/sin 449° = 2(sin 89°/sin 89°)
= 2(1) = 2 
Example 3: Find the value of 2 × (sin 44.5° cos 44.5°). [Hint: Use sin 89° = 0.9998]
Solution:
Using the sin 2a formula,
2 sin 44.5° cos 44.5° = sin(2 × 44.5°) = sin 89°
∵ sin 89° = 0.9998
⇒ 2 × (sin 44.5° cos 44.5°) = 0.9998
FAQs on Sin 89 Degrees
What is Sin 89 Degrees?
Sin 89 degrees is the value of sine trigonometric function for an angle equal to 89 degrees. The value of sin 89° is 0.9998 (approx).
What is the Value of Sin 89° in Terms of Cosec 89°?
Since the cosecant function is the reciprocal of the sine function, we can write sin 89° as 1/cosec(89°). The value of cosec 89° is equal to 1.00015.
What is the Value of Sin 89 Degrees in Terms of Tan 89°?
We know, using trig identities, we can write sin 89° as tan 89°/√(1 + tan²(89°)). Here, the value of tan 89° is equal to 57.289961.
How to Find Sin 89° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 89° can be given in terms of other trigonometric functions as:
 ± √(1cos²(89°))
 ± tan 89°/√(1 + tan²(89°))
 ± 1/√(1 + cot²(89°))
 ± √(sec²(89°)  1)/sec 89°
 1/cosec 89°
☛ Also check: trigonometric table
How to Find the Value of Sin 89 Degrees?
The value of sin 89 degrees can be calculated by constructing an angle of 89° with the xaxis, and then finding the coordinates of the corresponding point (0.0175, 0.9998) on the unit circle. The value of sin 89° is equal to the ycoordinate (0.9998). ∴ sin 89° = 0.9998.
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