Trigonometry Table (0° to 360°): Formulas, Ratios, and Values

Trigonometry Table

A trigonometry table provides the values of trigonometric functions for standard angles, including 0°, 30°, 45°, 60°, and 90°, as well as quadrant angles like 180°, 270°, and 360°. Trigonometry is a fundamental branch of mathematics focusing on the relationships between triangle sides and angles. Mastering this table is vital for Class 10, 11, and 12 mathematics, as well as various competitive entrance examinations. Understanding these values is the first step toward proficiency in trigonometry.

Trigonometry Table 0° to 360°

The trigonometric ratio table allows you to quickly identify values for standard and extended angles. There are six primary trigonometric ratios: sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). Memorizing these ratios is essential for solving geometric and algebraic problems across all high school grade levels and competitive tests. Let's explore the complete trigonometry table and function values from 0° to 360°.

Trigonometry 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	∞	0	∞	0
cot	∞	√3	1	1/√3	0	∞	0	∞
cosec	∞	2	√2	2/√3	1	∞	-1	∞
sec	1	2/√3	√2	2	∞	-1	∞	1

 

Trigonometry Table Tricks

Memorizing the trigonometry table is a powerful shortcut for solving complex problems. It is remarkably easy to learn the standard values for angles between 0° and 90° when you understand the underlying trigonometry formulas. The table is derived directly from these core mathematical identities. Below, we provide effective tips and formulas to help you master these values.

1. sin (90°− θ) = cos θ
2. cos (90°− θ) = sin θ
3. tan (90°− θ) = cot θ
4. cot (90°− θ) = tan θ
5. cosec (90°− θ) = sec θ
6. sec (90°− θ) = cosec θ
7. 1/sin θ = cosec θ
8. 1/cos θ = sec θ
9. 1/tan θ = cot θ

Trigonometry Table Chart

The values for 0°, 30°, 45°, 60°, and 90° are considered standard angles and are frequently required for academic assessments. By using our trigonometry table chart, you can streamline your calculations and improve your speed. You may download the chart below for quick reference and practice.

Trigonometry Table for Trigonometric Functions

There are six primary trigonometric functions, namely: Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent. These are abbreviated as sin, cos, tan, sec, cosec, and cot. Below, we detail the values for each of these functions.

Trigonometry Table for sin

The sine function table starts with sin 0° = 0 and rises to sin 90° = 1. Intermediate values include sin 30° = 1/2 and sin 45° = 1/√2.

Angles (In Degrees)	0°	30°	45°	60°	90°	180°	270°	360°
sin	0	1/2	1/√2	√3/2	1	0	-1	0

Trigonometry Table for cos

The cosine function is the inverse of the sine function for angles between 0° and 90°. For example, cos 0° = 1 and cos 90° = 0.

Angles (In Degrees)	0°	30°	45°	60°	90°	180°	270°	360°
cos	1	√3/2	1/√2	1/2	0	-1	0	1

Trigonometry Table for tan

The tangent table provides values such as tan 30° = 1/√3 and tan 60° = √3, essential for calculating slopes and heights in geometry.

Angles (In Degrees)	0°	30°	45°	60°	90°	180°	270°	360°
tan	0	1/√3	1	√3	∞	0	∞	0

Trigonometry Table for cot

The cotangent function acts as the reciprocal of tangent. For instance, cot 30° = √3 and cot 60° = 1/√3.

Angles (In Degrees)	0°	30°	45°	60°	90°	180°	270°	360°
cot	∞	√3	1	1/√3	0	∞	0	∞

Trigonometry Table for cosec

The cosecant function is the reciprocal of sine. Key values include cosec 45° = √2 and cosec 30° = 2.

Angles (In Degrees)	0°	30°	45°	60°	90°	180°	270°	360°
cosec	∞	2	√2	2/√3	1	∞	-1	∞

Trigonometry Table for sec

The secant function is the reciprocal of cosine. Notable values are sec 0° = 1, sec 30° = 2, and sec 45° = √2.

Angles (In Degrees)	0°	30°	45°	60°	90°	180°	270°	360°
sec	1	2/√3	√2	2	∞	-1	∞	1

Examples Related Trigonometry Table

Q1. Given that sin A = 0.66 at 40°, at what other angle will sin A again equal 0.66?

Solution: Since the sine function is periodic and repeats its values every 360°.

Applying this periodic property, we calculate:

sin A remains constant at 40° + 360° = 400°.

Therefore, at 400°, sin A will return to 0.66.

 

Q2. What is the lowest angle (in radians) where sin A equals cos A?

Solution: The values of sin A and cos A coincide at 45°, which is equal to Π/4 radians.

 

Q3. If tan x = 0.72, what is the value of cot x?

Solution: Since tan x = 1/cot x,

the value of cot x = 1/tan x.

Therefore, cot x = 1/0.72.

 

Q4. If sin(A+B) = 1/2 and sin(A-B) = 1/√2, solve for angles A and B in degrees.

Solution: Given sin(A+B) = 1/2.

We know sin 30° = 1/2.

Therefore, sin(A+B) = sin 30°.

A+B = 30° ---------- (i)

sin(A-B) = 1/√2.

We know sin 45° = 1/√2.

Therefore, sin(A-B) = sin 45°.

A-B = 45° ---------------(ii)

Adding (i) and (ii) gives:

(A+B) + (A-B) = 30° + 45°

2A = 75°

A = 75/2°

A = 37.5°

Substituting A into equation (i):

37.5° + B = 30°

B = 30° - 37.5°

Hence, B = -7.5°