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 to lớn find the value of sin 0 degrees with examples.
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Sin 0°: 0Sin (-0 degrees): 0Sin 0° in radians: sin (0π) or sin (0 . . .)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 khổng lồ 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 lớn 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 Circle
Sin 0° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 0 degrees as:
± √(1-cos²(0°))± chảy 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 to 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 size 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 và r.Hence the value of sin 0° = y = 0
☛ Also Check:
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, and 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.
How 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 to lớn 1.
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In trigonometry, there are three major or primary function, Sine, Cosine và Tangent, which are used to lớn find the angles and length of the right-angled triangle. Before discussing Sin 0, let us know about Sine function.Sine function defines a relation between the angle and perpendicular side & hypotenuse side. Or you can sin theta (the angle formed between the hypotenuse và adjacent side) is equal khổng lồ the ratio of perpendicular & hypotenuse of a right-angled triangle.
Let us discuss more of the trigonometric sine functions here in this article.
Sine Definition In Terms of Sin 0
As we have already discussed, the sin of angle theta is a ratio of the length of the opposite side, perpendicular & hypotenuse of the right-angled triangle.
Sin θ =Opposite Side/Hypotenuse
= Perpendicular/Hypotenuse
Now if we want to calculate sin 0 degrees value, we have to kiểm tra the coordinates point on x và y plane. Sin 0 signifies that the value of x coordinate is 1 và the value of y coordinate is 0,i.e. (x,y) is (1,0). That means the value of the opposite side or perpendicular is zero và the value of hypotenuse is 1. So if we place the values in sin ratio for θ=00 , perpendicular side= 1 and hypotenuse as 0, then we get,
Sin 00 =0/1
Or
Sin 00 = 0
From the above equation, we have yield sin 0 degrees value. Now let us write other sin degrees or radians values for one full revolution, in a table.
| Sine Degrees/Radians | Values |
| Sin 00 | 0 |
| Sin 300 or Sin π/6 | 1/2 |
| Sin 450 or Sin π/4 | (eginarrayl1/sqrt2endarray ) |
| Sin 600 or Sin π/3 | (eginarraylsqrt3/2endarray ) |
| Sin 900 or Sin π/2 | 1 |
| Sin 180°c or Sin π | 0 |
| Sin 270° or Sin 3π/2 | -1 |
| Sin 360° or Sin 2π | 0 |
If we write opposite of the value of Sin degrees, we get the values of cos degrees. Because, Sin θ=1/Cos θ
Therefore we can write,
Sin 00= Cos 900=0
Sin 300=Cos 600=½
Sin 450=Cos 450 = 1/√2
Sin 600=Cos 300= √3/2
Sin 900=Cos 00=1
In the same way, we can write the values for rã degrees.
Tan θ=Sin θ/Cos θ
Therefore,
Tan 00=Sin 00/Cos 00=0
Tan 300=Sin 300/Cos 300= √3/2
Tan 450=Sin 450/Cos 450=1
Tan 600=Sin 600/Cos 600=√3
Tan 900=Sin 900/Cos 900=Undefined
We learned about sin theta 0 degrees value along with other degree values here, this far. Also, derived the value for cos degree and tan degrees with respect sin degrees. In the same way, we can find other trigonometric ratios like sec, cosec & cot.
Based on these values, we can draw the trigonometry table,
| Angle | 00 | 300 | 450 | 600 | 900 | 1800 | 2700 | 3600 |
| Sin A | 0 | 1/2 | (eginarrayl1/sqrt2endarray ) (eginarraylsqrt3/2endarray ) | 1 | 0 | -1 | 0 | |
| Cos A | 1 | (eginarraylsqrt3/2endarray ) (eginarrayl1/sqrt2endarray ) | 1/2 | 0 | -1 | 0 | 1 | |
| Tan A | 0 | 1/ (eginarraylsqrt3endarray ) | 1 | (eginarraylsqrt3endarray ) | Undefined | 0 | Undefined | 0 |
Example: Find the value of Sin 900+Cos 900
Solution: As we know, Sin 900=1
And Cos 900=0
Therefore, Sin 900+Cos 900 = 1+0 = 1
Example: Find the value of Sin 270°+2Tan 450
Solution: Sin 270°= -1
And tung 450=1
Therefore, Sin 270°+2Tan 450 = -1+2*1 = -1+2 = 1
Learn more about trigonometric functions and download BYJU’S-The Learning phầm mềm for a better experience.
| MATHS Related Links | |
| Trigonometric Ratios of Complementary Angles | Trigonometric Functions |
| Trigonometric Ratios Of Standard Angles | Trigonometric Equations |
