Sin 495 Degrees
The value of sin 495 degrees is 0.7071067. . .. Sin 495 degrees in radians is written as sin (495° × π/180°), i.e., sin (11π/4) or sin (8.639379. . .). In this article, we will discuss the methods to find the value of sin 495 degrees with examples.
- Sin 495°: 0.7071067. . .
- Sin 495° in fraction: 1/√2
- Sin (-495 degrees): -0.7071067. . .
- Sin 495° in radians: sin (11π/4) or sin (8.6393797 . . .)
What is the Value of Sin 495 Degrees?
The value of sin 495 degrees in decimal is 0.707106781. . .. Sin 495 degrees can also be expressed using the equivalent of the given angle (495 degrees) in radians (8.63937 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 495 degrees = 495° × (π/180°) rad = 11π/4 or 8.6393 . . .
∴ sin 495° = sin(8.6393) = 1/√2 or 0.7071067. . .
Explanation:
For sin 495°, the angle 495° > 360°. Given the periodic property of the sine function, we can represent it as sin(495° mod 360°) = sin(135°). The angle 495°, coterminal to angle 135°, is located in the Second Quadrant(Quadrant II).
Since sine function is positive in the 2nd quadrant, thus sin 495 degrees value = 1/√2 or 0.7071067. . .
Similarly, sin 495° can also be written as, sin 495 degrees = (495° + n × 360°), n ∈ Z.
⇒ sin 495° = sin 855° = sin 1215°, and so on.
Note: Since, sine is an odd function, the value of sin(-495°) = -sin(495°).
Methods to Find Value of Sin 495 Degrees
The sine function is positive in the 2nd quadrant. The value of sin 495° is given as 0.70710. . .. We can find the value of sin 495 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Sin 495 Degrees Using Unit Circle
To find the value of sin 495 degrees using the unit circle, represent 495° in the form (1 × 360°) + 135° [∵ 495°>360°] ∵ sine is a periodic function, sin 495° = sin 135°.
- Rotate ‘r’ anticlockwise to form a 135° or 495° angle with the positive x-axis.
- The sin of 495 degrees equals the y-coordinate(0.7071) of the point of intersection (-0.7071, 0.7071) of unit circle and r.
Hence the value of sin 495° = y = 0.7071 (approx)
Sin 495° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 495 degrees as:
- ± √(1-cos²(495°))
- ± tan 495°/√(1 + tan²(495°))
- ± 1/√(1 + cot²(495°))
- ± √(sec²(495°) - 1)/sec 495°
- 1/cosec 495°
Note: Since 495° lies in the 2nd Quadrant, the final value of sin 495° will be positive.
We can use trigonometric identities to represent sin 495° as,
- sin(180° - 495°) = sin(-315°)
- -sin(180° + 495°) = -sin 675°
- cos(90° - 495°) = cos(-405°)
- -cos(90° + 495°) = -cos 585°
☛ Also Check:
FAQs on Sin 495 Degrees
What is Sin 495 Degrees?
Sin 495 degrees is the value of sine trigonometric function for an angle equal to 495 degrees. The value of sin 495° is 1/√2 or 0.7071 (approx).
What is the Exact Value of sin 495 Degrees?
The exact value of sin 495 degrees can be given accurately up to 8 decimal places as 0.70710678 and 1/√2 in fraction.
What is the Value of Sin 495 Degrees in Terms of Cot 495°?
We can represent the sine function in terms of the cotangent function using trig identities, sin 495° can be written as 1/√(1 + cot²(495°)). Here, the value of cot 495° is equal to -0.99999.
How to Find Sin 495° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 495° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(495°))
- ± tan 495°/√(1 + tan²(495°))
- ± 1/√(1 + cot²(495°))
- ± √(sec²(495°) - 1)/sec 495°
- 1/cosec 495°
☛ Also check: trigonometry table
How to Find the Value of Sin 495 Degrees?
The value of sin 495 degrees can be calculated by constructing an angle of 495° with the x-axis, and then finding the coordinates of the corresponding point (-0.7071, 0.7071) on the unit circle. The value of sin 495° is equal to the y-coordinate (0.7071). ∴ sin 495° = 0.7071.