Sin 65 Degrees
The value of sin 65 degrees is 0.9063077. . .. Sin 65 degrees in radians is written as sin (65° × π/180°), i.e., sin (13π/36) or sin (1.134464. . .). In this article, we will discuss the methods to find the value of sin 65 degrees with examples.
 Sin 65°: 0.9063077. . .
 Sin (65 degrees): 0.9063077. . .
 Sin 65° in radians: sin (13π/36) or sin (1.1344640 . . .)
What is the Value of Sin 65 Degrees?
The value of sin 65 degrees in decimal is 0.906307787. . .. Sin 65 degrees can also be expressed using the equivalent of the given angle (65 degrees) in radians (1.13446 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 65 degrees = 65° × (π/180°) rad = 13π/36 or 1.1344 . . .
∴ sin 65° = sin(1.1344) = 0.9063077. . .
Explanation:
For sin 65 degrees, the angle 65° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 65° value = 0.9063077. . .
Since the sine function is a periodic function, we can represent sin 65° as, sin 65 degrees = sin(65° + n × 360°), n ∈ Z.
⇒ sin 65° = sin 425° = sin 785°, and so on.
Note: Since, sine is an odd function, the value of sin(65°) = sin(65°).
Methods to Find Value of Sin 65 Degrees
The sine function is positive in the 1st quadrant. The value of sin 65° is given as 0.90630. . .. We can find the value of sin 65 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Sin 65° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 65 degrees as:
 ± √(1cos²(65°))
 ± tan 65°/√(1 + tan²(65°))
 ± 1/√(1 + cot²(65°))
 ± √(sec²(65°)  1)/sec 65°
 1/cosec 65°
Note: Since 65° lies in the 1st Quadrant, the final value of sin 65° will be positive.
We can use trigonometric identities to represent sin 65° as,
 sin(180°  65°) = sin 115°
 sin(180° + 65°) = sin 245°
 cos(90°  65°) = cos 25°
 cos(90° + 65°) = cos 155°
Sin 65 Degrees Using Unit Circle
To find the value of sin 65 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form a 65° angle with the positive xaxis.
 The sin of 65 degrees equals the ycoordinate(0.9063) of the point of intersection (0.4226, 0.9063) of unit circle and r.
Hence the value of sin 65° = y = 0.9063 (approx)
☛ Also Check:
Examples Using Sin 65 Degrees

Example 1: Using the value of sin 65°, solve: (1cos²(65°)).
Solution:
We know, (1cos²(65°)) = (sin²(65°)) = 0.8214
⇒ (1cos²(65°)) = 0.8214 
Example 2: Find the value of sin 65° if cosec 65° is 1.1033.
Solution:
Since, sin 65° = 1/csc 65°
⇒ sin 65° = 1/1.1033 = 0.9063 
Example 3: Simplify: 2 (sin 65°/sin 425°)
Solution:
We know sin 65° = sin 425°
⇒ 2 sin 65°/sin 425° = 2(sin 65°/sin 65°)
= 2(1) = 2
FAQs on Sin 65 Degrees
What is Sin 65 Degrees?
Sin 65 degrees is the value of sine trigonometric function for an angle equal to 65 degrees. The value of sin 65° is 0.9063 (approx).
How to Find Sin 65° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 65° can be given in terms of other trigonometric functions as:
 ± √(1cos²(65°))
 ± tan 65°/√(1 + tan²(65°))
 ± 1/√(1 + cot²(65°))
 ± √(sec²(65°)  1)/sec 65°
 1/cosec 65°
☛ Also check: trigonometry table
What is the Value of Sin 65° in Terms of Cosec 65°?
Since the cosecant function is the reciprocal of the sine function, we can write sin 65° as 1/cosec(65°). The value of cosec 65° is equal to 1.10337.
How to Find the Value of Sin 65 Degrees?
The value of sin 65 degrees can be calculated by constructing an angle of 65° with the xaxis, and then finding the coordinates of the corresponding point (0.4226, 0.9063) on the unit circle. The value of sin 65° is equal to the ycoordinate (0.9063). ∴ sin 65° = 0.9063.
What is the Value of Sin 65 Degrees in Terms of Cot 65°?
We can represent the sine function in terms of the cotangent function using trig identities, sin 65° can be written as 1/√(1 + cot²(65°)). Here, the value of cot 65° is equal to 0.46630.