Full Trigonometry Table with Formulas: 0° to 360°

As we know students who were in school think trigonometry is hard but the full trigonometry table makes solving trigonometry much easier. In this article we will let you know the full trigonometry table with formulas, values from 0 degree to 360 degree, a radians table along with the inverse trigonometry table. This trigonometry table is best for the students who are in class 9 to 12 as well as who are learning trigonometry.

☰ Table of Contents

What Is a Trigonometry Table?

A trigonometry table lists the values of sine (sin), cosine (cos), tangent (tan), cosecant (cosec), secant (sec) and cotangent (cot) for common angles. Students use this table to solve the problems faster without using a calculator.

Trigonometry Table Formula (Basic Ratios)

For a right-angled triangle:

sin θ = Opposite ÷ Hypotenuse
cos θ = Adjacent ÷ Hypotenuse
tan θ = Opposite ÷ Adjacent = sin θ ÷ cos θ
cosec θ = 1 ÷ sin θ
sec θ = 1 ÷ cos θ
cot θ = 1 ÷ tan θ = cos θ ÷ sin θ

Key identities to remember:

sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ

Trigonometry Table 0 to 90 Degree

This trigonometry table is imp for class 10. Learn it well.

Angle	0°	30°	45°	60°	90°
sin	0	1/2	1/√2	√3/2	1
cos	1	√3/2	1/√2	1/2	0
tan	0	1/√3	1	√3	Not defined
cosec	Not defined	2	√2	2/√3	1
sec	1	2/√3	√2	2	Not defined
cot	Not defined	√3	1	1/√3	0

Easy trick for sin: write 0, 1, 2, 3, 4. Divide each by 4 and take the square root. You get 0, 1/2, 1/√2, √3/2 and 1. For cos, write the same values in reverse order.

Trigonometry Table 0 to 180 Degree

For angles between 90° and 180°, use these formulas:

sin (180° − θ) = sin θ
cos (180° − θ) = −cos θ
tan (180° − θ) = −tan θ

Angle	0°	30°	45°	60°	90°	120°	135°	150°	180°
sin	0	1/2	1/√2	√3/2	1	√3/2	1/√2	1/2	0
cos	1	√3/2	1/√2	1/2	0	−1/2	−1/√2	−√3/2	−1
tan	0	1/√3	1	√3	N/D	−√3	−1	−1/√3	0

Trigonometry Table 0 to 360 Degree (With Radians)

This 360 degree trigonometry table also works as a trigonometry table in radians. It is very useful for trigonometry table class 11.

Degree	Radian	sin	cos	tan
0°	0	0	1	0
30°	π/6	1/2	√3/2	1/√3
45°	π/4	1/√2	1/√2	1
60°	π/3	√3/2	1/2	√3
90°	π/2	1	0	N/D
120°	2π/3	√3/2	−1/2	−√3
135°	3π/4	1/√2	−1/√2	−1
150°	5π/6	1/2	−√3/2	−1/√3
180°	π	0	−1	0
210°	7π/6	−1/2	−√3/2	1/√3
225°	5π/4	−1/√2	−1/√2	1
240°	4π/3	−√3/2	−1/2	√3
270°	3π/2	−1	0	N/D
300°	5π/3	−√3/2	1/2	−√3
315°	7π/4	−1/√2	1/√2	−1
330°	11π/6	−1/2	√3/2	−1/√3
360°	2π	0	1	0

N/D means not defined.

Radian formula: Radian = Degree × π/180. Degree = Radian × 180/π.

How to Find Values for Any Angle (0° to 360°)

Use the ASTC rule (All, Sin, Tan, Cos):

Quadrant 1 (0°–90°): All ratios are positive.
Quadrant 2 (90°–180°): Only sin and cosec are positive.
Quadrant 3 (180°–270°): Only tan and cot are positive.
Quadrant 4 (270°–360°): Only cos and sec are positive.

Reduction formulas:

sin (360° − θ) = −sin θ
cos (360° − θ) = cos θ
tan (360° − θ) = −tan θ
sin (180° + θ) = −sin θ
cos (180° + θ) = −cos θ
tan (180° + θ) = tan θ

Example: Find sin 210°. Write 210° = 180° + 30°. So sin 210° = −sin 30° = −1/2.

Inverse Trigonometry Table

Inverse trigonometry gives you the angle when you know the ratio. It is written as sin⁻¹, cos⁻¹ and tan⁻¹.

Function	Domain	Range (Principal Value)
sin⁻¹ x	−1 to 1	−π/2 to π/2
cos⁻¹ x	−1 to 1	0 to π
tan⁻¹ x	All real numbers	−π/2 to π/2 (not including ends)

Common inverse values:

x	sin⁻¹ x	cos⁻¹ x	tan⁻¹ x
0	0°	90°	0°
1/2	30°	60°	N/A
1/√2	45°	45°	N/A
√3/2	60°	30°	N/A
1	90°	0°	45°

Useful formulas:

sin⁻¹ x + cos⁻¹ x = π/2
tan⁻¹ x + cot⁻¹ x = π/2
sin⁻¹ (−x) = −sin⁻¹ x

Tips to Remember the Trigonometry Table

Learn the 0° to 90° table first. All other values come from it.
Use the ASTC rule to find the sign.
Draw the unit circle. It helps you see why values repeat.
Practice with five questions every day.
Revise the identities weekly.

Frequently Asked Questions

What is the value of sin 90°?

It is 1.

What is tan 90°?

It is not defined, because cos 90° is 0 and you cannot divide by zero.

Which table is needed for class 10?

0° to 90° table.

Which table is needed for class 11?

0° to 360° table along with radians, and inverse functions.