Trigonometric Symbols are mathematical symbols used to represent angles, trigonometric functions, inverse functions, and other quantities commonly used in trigonometry.
Common Trigonometric Symbols
In trigonometry, there are many functions used to relate angles within a right triangle to its various lengths or ratios.
Trigonometric Symbol | Trigonometric Symbol Name | Explanation |
|---|---|---|
θ | Theta | It is used to represent an angle in trigonometric equations. |
α | Alpha | Represents an angle |
sin | Sine | It is represented as "sin(θ)." |
cos | Cosine | It is represented as "cos(θ)." |
tan | Tangent | It is represented as "tan(θ)." |
csc | Cosecant | The angle of cosecant is the reciprocal of the sine, csc(θ) = 1/sin(θ). |
sec | Secant | The angle of a secant is the reciprocal of the cosine, sec(θ) = 1/cos(θ). |
cot | Cotangent | The angle of cotangent is the reciprocal of the tangent, cot(θ) = 1/tan(θ). |
arcsin x or sin⁻¹(x) | Arcsine function or Inverse sine | It is used to find the angle for a given trigonometric ratio |
arccos x or cos⁻¹(x) | Arccos function or Inverse cosine | It is used to find the angle for a given trigonometric ratio |
arctan x or tan⁻¹(x) | Arctan function or Inverse tan | It is used to find the angle for a given trigonometric ratio |
π | Pi | It is used in trigonometry to express angles in radians. |
r | Radius | In polar coordinates, r represents the distance from the origin to a point, which is used in trigonometry when dealing with polar coordinates. |
Δ | Delta | It is used to represent the change in an angle, such as Δθ |
Trigonometric Symbols in Right-Angled Triangle
There are 6 basic trigonometric relations that form the basics of trigonometry. These 6 trigonometric relations are ratios of all the different possible combinations in a right-angled triangle.
Trigonometric Symbols of θ | Trigonometric Function in Right-Angled Triangle |
|---|---|
Sine (sin θ) | sin θ = perpendicular/hypotenuse |
Cosine (cos θ) | cos θ = base/hypotenuse |
Tangent (tan θ) | tan θ = perpendicular/base |
Cosecant (csc θ) | csc θ = hypotenuse/perpendicular |
secant (sec θ) | sec θ = hypotenuse/base |
cotangent (cot θ) | cot θ = base/hypotenuse |
Symbols Used in Radian Measure
Angles can be measured in degrees or radians. Trigonometry frequently uses radians because many mathematical formulas are simpler in radian form.
Pi Symbol (π): The symbol π (Pi) is approximately equal to \pi
The relationship between degrees and radians is 180^\circ=\pi
Common Angle Conversions
The symbol π is fundamental in trigonometry and circular geometry.
| Degrees (°) | Radians |
|---|---|
| 0° | 0 |
| 30° | |
| 45° | |
| 60° | |
| 90° | |
| 120° | |
| 180° | |
| 360° |
Symbols Used in Polar Coordinates
Polar coordinates describe the position of a point using a distance and an angle.
The two main symbols are the following:
- r = distance from origin
- θ = Angle measured from the positive x-axis
A point in polar coordinates is written as (r,\theta).
Solved Examples
Example 1: What does the symbol "sec θ" represent?
Secant is the reciprocal of cosine.
\sec\theta=\frac{1}{\cos\theta}
Example 2: Find the value of \sin^{-1}\left(\frac{1}{2}\right).
The angle whose sine value is 1/2 is :
\sin^{-1}\left(\frac{1}{2}\right)=30^\circ
Example 3: Convert 180° into radians.
180^\circ=\pi \text{ radians}
Practice Questions
- Which symbol is commonly used to represent an angle in trigonometry?
- What is the reciprocal of sin θ?
- What is the reciprocal of tan θ?
- Which symbol represents the radius in polar coordinates?
- What is the value of 360° in radians?
