Trigonometry Table

Trigonometry Table 0 to 360: Trigonometry is a branch in mathematics, which involves the study of the relationship involving the length and angles of a triangle. It is generally associated with a right-angled triangle, where one of the angles is always 90 degrees. The taIt has a wide number of application in other fields of mathematics. Many geometric calculations can be easily figured out using the table of trigonometric functions and formulas as well.

The Trigonometrical ratios table helps to find the values of trigonometric standard angles such as 0°, 30°, 45°, 60° and 90°. It consists of trigonometric ratios – sine, cosine, tangent, cosecant, secant, cotangent. These ratios can be written in short as sin, cos, tan, cosec, sec and cot. The values of trigonometrical ratios of standard angles are very important to solve the trigonometrical problems. Therefore, it is necessary to remember the value of the trigonometrical ratios of these standard angles.

The trigonometric table is useful in the number of areas. It is essential for navigation, science, and engineering. This table was effectively used in the pre-digital era, even before the existence of pocket calculators. Further, the table led to the development of the first mechanical computing devices. Another important application of trigonometric tables is for Fast Fourier Transform (FFT) algorithms.

 

Trigonometry Ratio Table
Angles (In Degrees) 30° 45° 60° 90° 180° 270° 360°
Angles (In Radians) π/6 π/4 π/3 π/2 π 3π/2
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 1
cot √3 1 1/√3 0 0
csc 2 √2 2/√3 1 -1
sec 1 2/√3 √2 2 -1 1

Tricks To Remember Trigonometry Table

Remembering the trigonometry table will help in many ways, and it is easy to remember the table. If you know the trigonometry formulas than remembering the trigonometry table is very easy. The Trigonometry ratio table id depended upon the trigonometry formulas in a similar way all the functions of trigonometry are depended on each aspect and interlinked with each other.

Below are the few steps to memorize the trigonometry table.

Before beginning try to remember these values, recall and remember below trigonometry formulas.

  • sin x = cos (90°-x)
  • cos x = sin (90°-x)
  • tan x = cot (90°-x)
  • cot x = tan (90°-x)
  • sec x = cot (90°-x)
  • cot x = sec (90°-x)
  • 1/sin x = csc x
  • 1/cos x = sec x
  • 1/tan x = cot x

Steps to Create Trigonometry Table:

Step 1:

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

Step 2: Determine the value of sin.

To determine the value of sin divide all the value by 4 with all root. See the example below.

To determine the value of sin 0°

\(\sqrt{\frac{0}{4}}=0\)

In a similar way, dividing all the angles with the value of sin. The answer would be.

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

Step 3: Determine the value of cos.

The cos-value is the opposite angle of sin angle. To determine the value of cos divide by 4 in opposite sequence of sin. For this divide of 4 by 4 with all root such as. See the example below.

To determine the value of cos 0°

\(\sqrt{\frac{4}{4}}=1\)

In a similar way, dividing all the angles with the value of cos. The answer would be.

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

Step 4: Determine the value of tan.

The tan is equal to sin divided by cos. tan = sin/cos. To determine the value of tan on  divide the value of sin on  by the value of cos on  See example below.

tan 0°= 0/1 = 0

In a similar way, the table would be.

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

Step 5: Determine the value of cot.

The value of cot can be determined by all opposite value of tan. The value of tan on is the opposite of tan on . So the value will be:

cot 0°=1/0=Infinite or Not Defined

Same way, the table for a sec is below.

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

Step 6: Determine the value of cosec.

The value of cosec on is the opposite of sin on .

csc 0°= 1/0=Infinite or Not Defined

Same way, the table for cosec is below.

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

Step 7: Determine the value of sec.

The value of sec can be determined by all opposite value of cos. The value of sec on \(0^{\circ }\) is the opposite of cos on \(0^{\circ }\). So the value will be:

\(\sec 0^{\circ }=\frac{1}{1}=1\)

Same way, the table for sec is below.

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

 

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