The value of sin 6 degrees is 0.1045284. . .
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. Sin 6 degrees in radians is written as sin (6° × π/180°), i.e., sin (π/30) or sin (0.104719. . .). In this article, we will discuss the methods to lớn find the value of sin 6 degrees with examples.
What is the Value of Sin 6 Degrees?
We know, using degree khổng lồ radian conversion, θ in radians = θ in degrees × (pi/180°)⇒ 6 degrees = 6° × (π/180°) rad = π/30 or 0.1047 . . .∴ sin 6° = sin(0.1047) = 0.1045284. . .
Explanation:
For sin 6 degrees, the angle 6° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 6° value = 0.1045284. . .Since the sine function is a periodic function, we can represent sin 6° as, sin 6 degrees = sin(6° + n × 360°), n ∈ Z.⇒ sin 6° = sin 366° = sin 726°, & so on.Note: Since, sine is an odd function, the value of sin(-6°) = -sin(6°).
Methods to lớn Find Value of Sin 6 Degrees
The sine function is positive in the 1st quadrant. The value of sin 6° is given as 0.10452. . .. We can find the value of sin 6 degrees by:
Using Trigonometric FunctionsUsing Unit CircleSin 6° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 6 degrees as:
± √(1-cos²(6°))± chảy 6°/√(1 + tan²(6°))± 1/√(1 + cot²(6°))± √(sec²(6°) - 1)/sec 6°1/cosec 6°Note: Since 6° lies in the 1st Quadrant, the final value of sin 6° will be positive.
We can use trigonometric identities lớn represent sin 6° as,
sin(180° - 6°) = sin 174°-sin(180° + 6°) = -sin 186°cos(90° - 6°) = cos 84°-cos(90° + 6°) = -cos 96°Sin 6 Degrees Using Unit Circle
To find the value of sin 6 degrees using the unit circle:
Rotate ‘r’ anticlockwise to form a 6° angle with the positive x-axis.The sin of 6 degrees equals the y-coordinate(0.1045) of the point of intersection (0.9945, 0.1045) of unit circle and r.Hence the value of sin 6° = y = 0.1045 (approx)
☛ Also Check:
FAQs on Sin 6 Degrees
What is Sin 6 Degrees?
Sin 6 degrees is the value of sine trigonometric function for an angle equal to 6 degrees. The value of sin 6° is 0.1045 (approx).
How to Find the Value of Sin 6 Degrees?
The value of sin 6 degrees can be calculated by constructing an angle of 6° with the x-axis, & then finding the coordinates of the corresponding point (0.9945, 0.1045) on the unit circle. The value of sin 6° is equal to lớn the y-coordinate (0.1045). ∴ sin 6° = 0.1045.
How khổng lồ Find Sin 6° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 6° can be given in terms of other trigonometric functions as:
± √(1-cos²(6°))± tan 6°/√(1 + tan²(6°))± 1/√(1 + cot²(6°))± √(sec²(6°) - 1)/sec 6°1/cosec 6°☛ Also check: trigonometric table
What is the Exact Value of sin 6 Degrees?
The exact value of sin 6 degrees can be given accurately up lớn 8 decimal places as 0.10452846.
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What is the Value of Sin 6 Degrees in Terms of Cos 6°?
Using trigonometric identities, we can write sin 6° in terms of cos 6° as, sin(6°) = √(1-cos²(6°)). Here, the value of cos 6° is equal lớn 0.9945218.