Table of Contents
Value of Sin 180 – Formula, Sine Value Table, Sine 180 Degree and FAQs
Explain in Detail :What are Trigonometric Ratios?
Trigonometric ratios are ratios of the sides of a right triangle. The three most common ratios are sine, cosine, and tangent.
Sine Function Formula
The sine function is a mathematical function that is used to calculate the angle of a point on a unit circle from its x-coordinate. The sine function is also used to calculate the length of the opposite side of a given angle. The sine function is written as Sin(x) and is defined as follows:
Sin(x) = Opposite / Hypotenuse
Sine 180 Degree Derivation: Method 1
Now we can use the above expression (1) in terms of sine functions.
From the supplementary angle identity, we know that;
Sin (180 – Theta) = Sin Theta
Sin A = Sin (180° – A)
Therefore,
Sin ( 180° – A ) = Sin A
Sin ( 180° – 0° ) = Sin 0°
Sin 180° = 0 [Since the value Sin 0° is 0]
Hence, the value of sin pi is 0
Sine Pi Value Derivation: Method 2
From the expression (2),
Using complementary angle identity,
Sin A = cos (90°- A)
we can write the above expression as:
Sin 180°= cos (90° – 180°)
Sin 180°= cos (-90°)
Now, use opposite angle identity cos(-A) = cos A
Sin 180°= cos 90°
Sin 180°= 0 [Since the value of cos 90 degrees is 0]
Therefore, the value of sin 180 is 0.
Sin 180° = 0
Sine Value Table
The sine value table is a table of angles and their corresponding sine values.
The trigonometric ratios value for different angles and functions are as follows:
| Trigonometry Ratio Table | ||||||||
|---|---|---|---|---|---|---|---|---|
| Angles (In Degrees) | 0 | 30 | 45 | 60 | 90 | 180 | 270 | 360 |
| Angles (In Radians) | 0 | π/6 | π/4 | π/3 | π/2 | π | 3π/2 | 2π |
| sin | 0 | 1/2 | 1/√2 | √3/2 | 1 | 0 | −1 | 0 |
| cos | 1 | √3/2 | 1/√2 | 1/2 | 0 | −1 | 0 | 1 |
| tan | 0 | 1/√3 | 1 | √3 | Not Defined | 0 | Not Defined | 0 |
| cot | Not Defined | √3 | 1 | 1/√3 | 0 | Not Defined | 0 | Not Defined |
| cosec | Not Defined | 2 | √2 | 2/√3 | 1 | Not Defined | −1 | Not Defined |
| sec | 1 | 2/√3 | √2 | 2 | Not Defined | −1 | Not Defined | 1 |
Sine 180 Degree Derivation
A sine curve is a mathematical curve that describes a smooth oscillation. It is generated by plotting the sine of x-coordinates against the x-coordinates. A sine curve has a period of 2π, which means that it repeats its shape every 2π units. The curve typically peaks at the middle of its cycle and then gradually decreases to zero.
A sine curve can be derived from a right triangle. The length of the hypotenuse is the length of the curve. The length of the other two sides are the x- and y-coordinates of the curve. The sine of the angle between the hypotenuse and the x-axis is the x-coordinate of the curve. The sine of the angle between the hypotenuse and the y-axis is the y-coordinate of the curve.
Also Read: Value of Cos 120 Degree and Other Trigonometric Angles – Find Value of Cos 120
