The value of sin 0 degrees is 0. Sin 0 degrees in radians is written as sin (0° × π/180°), i.e., sin (0π) or sin (0). In this article, we will discuss the methods khổng lồ find the value of sin 0 degrees with examples.
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What is the Value of Sin 0 Degrees?
The value of sin 0 degrees is 0. Sin 0 degrees can also be expressed using the equivalent of the given angle (0 degrees) in radians (0 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)⇒ 0 degrees = 0° × (π/180°) rad = 0π or 0 . . .∴ sin 0° = sin(0) = 0
Explanation:
For sin 0 degrees, the angle 0° lies on the positive x-axis. Thus, sin 0° value = 0Since the sine function is a periodic function, we can represent sin 0° as, sin 0 degrees = sin(0° + n × 360°), n ∈ Z.⇒ sin 0° = sin 360° = sin 720°, and so on.Note: Since, sine is an odd function, the value of sin(-0°) = -sin(0°) = 0.
Methods to Find Value of Sin 0 Degrees
The value of sin 0° is given as 0. We can find the value of sin 0 degrees by:
Using Trigonometric FunctionsUsing Unit CircleSin 0° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 0 degrees as:
± √(1-cos²(0°))± tan 0°/√(1 + tan²(0°))± 1/√(1 + cot²(0°))± √(sec²(0°) - 1)/sec 0°1/cosec 0°Note: Since 0° lies on the positive x-axis, the final value of sin 0° will be 0.
We can use trigonometric identities lớn represent sin 0° as,
sin(180° - 0°) = sin 180°-sin(180° + 0°) = -sin 180°cos(90° - 0°) = cos 90°-cos(90° + 0°) = -cos 90°Sin 0 Degrees Using Unit Circle
To find the value of sin 0 degrees using the unit circle:
Draw the radius of the unit circle, r to form a 0° angle with the positive x-axis. We also know that for the sin 0°, the angle 0° corresponds lớn the point (1, 0) on the unit circle (as it is a point on the unit circle present on the x-axis).The sin of 0 degrees equals the y-coordinate(0) of the point of intersection(1, 0) of the unit circle & r.Hence the value of sin 0° = y = 0
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FAQs on Sin 0 Degrees
What is Sin 0 Degrees?
Sin 0 degrees is the value of sine trigonometric function for an angle equal lớn 0 degrees. The value of sin 0° is 0.
How lớn Find the Value of Sin 0 Degrees?
The value of sin 0 degrees can be calculated by constructing an angle of 0° with the x-axis, & then finding the coordinates of the corresponding point (1, 0) on the unit circle. The value of sin 0° is equal khổng lồ the y-coordinate (0). ∴ sin 0° = 0.
What is the Value of Sin 0° in Terms of Sec 0°?
Since the sine function can be represented using the secant function, we can write sin 0° as √(sec²(0°) - 1)/sec 0°. The value of sec 0° is equal to 1.
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How to lớn Find Sin 0° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 0° can be given in terms of other trigonometric functions as:
± √(1-cos²(0°))± tung 0°/√(1 + tan²(0°))± 1/√(1 + cot²(0°))± √(sec²(0°) - 1)/sec 0°1/cosec 0°☛ Also check: trigonometry table
What is the Value of Sin 0 Degrees in Terms of Cos 0°?
Using trigonometric identities, we can write sin 0° in terms of cos 0° as, sin(0°) = √(1-cos²(0°)). Here, the value of cos 0° is equal khổng lồ 1.