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
The Trigonometry Table contains angles in degrees and radians, that very easy to convert of degrees in radians and vice versa, radians in degrees.
Its collection of trigonometric values of various standard angles including 0 °, 30 °, 45 °, 60 °, 90 °, sometimes with other angles such as 180 °, 270 ° and 360 °.
Trigonometry Table has trigonometric functions – sine, cosine, tangent, coscent, secant, cotangent. 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.
Trigonometry Table Formula
| 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
Trigonometry table will help in many ways to remember Trigonometric Ratio.
Create a table with 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, cosec, sec, cot.
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 these three Formula
- sin (π − θ) = sin θ
- sin (π + θ) = -sin θ
- 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:
| 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 these three Formula
- cos(π−θ) = -cosθ
- cos(π+θ) = -cosθ
- 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 Sin like:
| 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.
| 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 Coscent Of Standard Angles
cot θ = cos θ/sin θ
Hence, the tan row can be generated.
| 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.
| 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 Cotangent Of Standard Angles
cosec θ = 1/sin θ
Hence, the tan row can be generated.
| 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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