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)
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|
|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.