Here is a Trigonometry Table for standard angles (0°, 30°, 45°, 60°, 90°), showing the values of sine, cosine, tangent, cosecant, secant, and cotangent:
Explanation:
- Sin (θ): Opposite side / Hypotenuse
- Cos (θ): Adjacent side / Hypotenuse
- Tan (θ): Opposite side / Adjacent side (Sin(θ) / Cos(θ))
- Cosec (θ): 1 / Sin(θ)
- Sec (θ): 1 / Cos(θ)
- Cot (θ): 1 / Tan(θ)
This table helps in solving various trigonometric problems by providing standard angle values for common trigonometric functions.
Trigonometry Table For It’s Functions
Here’s a Trigonometric Functions Table for standard angles (0°, 30°, 45°, 60°, 90°), covering the six primary trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent.
| Table of Trigonometric Functions | |||
| Function | Definition | Representation | Relationship to Sides of a Right Triangle |
| Sine | Ratio of perpendicular and hypotenuse | sinθ | Opposite side / Hypotenuse |
| Cosine | Ratio of base and hypotenuse | cosθ | Adjacent side / Hypotenuse |
| Tangent | Ratio of sine and cosine of an angle | tanθ | Opposite side / Adjacent side |
| Cosecant | Reciprocal of sin θ | cscθ or cosecθ | Hypotenuse / Opposite side |
| Secant | Reciprocal of cos θ | secθ | Hypotenuse / Adjacent side |
| Cotangent | Reciprocal of tan θ | cotθ | Adjacent side / Opposite side |
Trigonometric Formulas
Let’s learn about some trigonometry formulas related to Complementary and Supplementary Angles.
- Complementary Angles: Pair of angles whose sum is equal to 90°
- Supplementary Angles: Pair of angles whose sum is equal to 180°
Trig Identities of Complementary Angles
The identities of complementary angles are based on the relationship between the trigonometric functions of two angles that sum up to 90 degrees (or π/2 radians). These are known as co-function identities.
| Trigonometric Function | Identity |
| Sine | sin(90°−θ)=cosθ |
| Cosine | cos(90°−θ)=sinθ |
| Tangent | tan(90°−θ)=cotθ |
| Cotangent | cot(90°−θ)=tanθ |
| Secant | sec(90°−θ)=cscθ |
| Cosecant | cosec(90°−θ)=secθ |
Trig Identities of Supplementary Angles
The identities of supplementary angles relate to the trigonometric functions of two angles that sum up to 180 degrees (or π radians).
| Trigonometric Function | Identity |
| Sine | sin(180°−θ)=sinθ |
| Cosine | cos(180°−θ)=−cosθ |
| Tangent | tan(180°−θ)=−tanθ |
| Cotangent | cot(180°−θ)=−cotθ |
| Secant | sec(180°−θ)=−secθ |
| Cosecant | cosec(180°−θ)=cosecθ |
Conclusion
The trigonometry table provides a quick reference for the values of the six primary trigonometric functions—sine, cosine, tangent, cosecant, secant, and cotangent—for standard angles (0°, 30°, 45°, 60°, and 90°). These functions are essential in understanding the relationships between the angles and sides of right-angled triangles and are widely used in geometry, physics, engineering, and various fields of mathematics.