Trigonometry Table | Trigonometric Ratios Table

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles (right-angled triangles). It has a wide number of applications in other fields of Mathematics.

Its helps in finding the angles and missing sides of a right-angled triangle with the help of trigonometric ratios.

Trigonometry Table

Trigonometry table helps to find the values of trigonometric ratios of standard angles.

The table contains standard angles in degrees and radians, that very easy to convert of degrees to radians and vice versa. Various standard angles including 0°, 30°, 45°, 60°, 90°, sometimes with other angles such as 180°, 270° and 360°.

It consists of trigonometric ratios – sine, cosine, tangent, cotangent, coscent, secant. These ratios can be abbreviated as sin, cos, tan, cosec, sec, and cot.

The value of trigonometric ratios of standard angles is required to solve trigonometric problems. Therefore, it is necessary to remember the values ​​of trigonometric ratios of these standard angles.

Check Trigonometry Table for trigonometric ratios, trigonometric function values ​​for standard angles and Understand trigonometry table tricks.

Trigonometric Ratios Table

Trigonometric ratios table contains the value of trigonometric ratios at specific angles. These values are applicable in the right-angle triangle.

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

Simple Trick To Remember Trigonometric Ratio Table

Remembering values of standard angles can be difficult. But with the method described below you can easily remember the values of standard angles.

Create a table with a top row by listing angles such as 0 °, 30 °, 45 °, 60 °, 90 °, and write all trigonometric functions in the first column such as sin, cos, tan, cot, cosec, sec.

Determining Values Of Sine Of Standard Angles

• To determine the values ​​of sin of standard angles, Write the angles 0°, 30°, 45°, 60°, 90° in ascending order and assign them values 0, 1, 2, 3, 4 according to the order. 

So, 0° ⟶ 0 , 30° ⟶ 1, 45° ⟶ 2 , 60° ⟶ 3 , 90° ⟶ 4

• Then divide the values by 4 and square root the entire value.

√(0/4)=0, √(1/4)=1/2, √(2/4)=1/√2, √(3/4)=√3/2, √(4/4)=1

Now for the remaining three Formula 

1. sin (π − θ) = sin θ  
2. sin (π + θ) = -sin θ
3. sin (2π − θ) = -sin θ

Here, π=180°

• sin (180°− 0°) = sin (180) = sin 0° = 0
• sin (180° + 90°) = sin (270°) = -sin 90° = 1
• sin (360°− 0°) = sin (360°) = -sin 0° = 0

Now you will remember Trigonometry Table for Sin like:

Trigonometry Table for Sin

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

Determining Values Of Cosine Of Standard Angles

• To determine the values ​​of cos of standard angles, Write the angles 0°, 30°, 45°, 60°, 90° in ascending order and assign them values 4, 3, 2, 1, 0 according to the order. 

So, 0° ⟶ 4, 30° ⟶ 3, 45° ⟶ 2, 60° ⟶ 1, 90° ⟶ 0

• Then divide the values by 4 and square root the entire value.

√(4/4)=1, √(3/4)=√3/2, √(2/4)=1/√2, √(1/4)=1/2, √(0/4)=0

Now for the remaining three Formula 

1. cos(π−θ) = -cosθ
2. cos(π+θ) = -cosθ
3. cos(2π−θ) = cosθ

Here, π=180°

• cos (180°− 0°) = cos (180) = -cos 0° = -1
• cos (180° + 90°) = cos (270°) = -cos 90° = 0
• cos (360°− 0°) = cos (360°) = cos 0° = 1

Now you will remember Trigonometry Table for Cos like:

Trigonometry Table for Cos

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
cos	1	√3/2	1/√2	1/2	0	-1	0	1

Remember Trigonometry Formulas

Remember these trigonometry formulas to determining Values other ratios:

• sin θ= cos (90° – θ)
• cos θ= sin (90° – θ)
• tan θ = sin θ/cos θ = 1/cot θ = cot (90° – θ)
• cot θ = cos θ/sin θ = 1/tan θ = tan (90° – θ)
• sec θ = 1/cos θ = cosec (90° – θ)
• cosec θ = 1/sin θ = sec (90° – θ)

Determining Values Of Tangent Of Standard Angles

tan θ = sin θ/cos θ
Hence, the tan row can be generated.

Trigonometry Table for Tan

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	∞	0	∞	0

Determining Values Of Cotangent Of Standard Angles

cot θ = cos θ/sin θ
Hence, the tan row can be generated.

Trigonometry Table for Cot

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
cot	∞	√3	1	1/√3	0	∞	0	∞

Determining Values Of Secant Of Standard Angles

sec θ = 1/cos θ
Hence, the tan row can be generated.

Trigonometry Table for Sec

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
sec	0	2/√3	√2	2	∞	-1	∞	-1

Determining Values Of Cosecant Of Standard Angles

cosec θ = 1/sin θ
Hence, the tan row can be generated.

Trigonometry Table for Cosec

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
cosec	∞	2	√2	2/√3	1	∞	-1	∞

Trigonometry Table | Trigonometric Ratios Table (Image)

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