Trigonometric Table 

The trigonometric ratios table helps in finding the values of standard angles such as 0°, 30°, 45°, 60°, and 90°. Trigonometry table comprises trigonometric ratios – sine, cosine, tangent, cosecant, secant, cotangent. These ratios, in short, are written as sin, cos, tan, cosec, sec, and cot. The values of trigonometric ratios of standard angles are essential in solving trigonometry problems. 

Trigonometry deals with the measurement of angles and problems related to angles. The term trigonometry is derived from a Latin word. Trigonometry makes use of the relationship between the angles and sides of a triangle.

To remember this easily remember the word "SOHCAHTOA"! 

• SOH

Sine = Opposite / Hypotenuse

• CAH

Cosine = Adjacent / Hypotenuse

• TOA

Tangent = Opposite / Adjacent

Standard Angles

The trigonometric values for the angles 0°, 30°, 45°, 60°, and 90° are commonly used to solve the trigonometry problems. These values are associated with the measurement of the lengths and the angles of a right-angle triangle.  Thus, 0°, 30°, 45°, 60°, and 90° are called the standard angles in trigonometry.

Using the above table, values of sin π/6, cos π/6, tan π/6, sin π/4, cos π/4, tan π/4, sin π/3, cos π/3, tan π/3, sin π/2, cos π/2, and tan π/2 in radians could be easily found out. A trigonometry table has wide application in fields like science and engineering.

A few key points that can be noted in the trigonometric table are,

• The values of complementary angles present like 30° and 60° can be computed using complementary formulas for the various trigonometric ratios. 
• The value for some ratios given as ∞. The reason for this is that while computing the values, a "0" appears in their denominator, so the value becomes undefined and is said to be equivalent to infinity.
• There is a sign change in the values in various places under 90°, 180°, etc. This is due to the change in different quadrants. 

• Step 3: Determining the value of cos. sin (90° – x) = cos x. Use this formula to compute values for cos x. For example, cos 45° = sin (90° – 45°) = sin 45°. Similarly, cos 30° = sin (90°-30°) = sin 60°. Using this, you can easily find out the value of cos function as,

• Step 4: Determining the value of tan. (tan x = sin x/cos x). Hence, the value of tan function can be generated as,

• Step 5: Determining the value of cot. (cot x = 1/tan x). Use the relation to generate the cot function as,

• Step 6: Determining the value of cosec. (cosec x = 1/sin x)

• Step 7: Determining the value of sec. (sec x = 1/cos x) 

The following table covers the value of trigonometric ratios for all basic angles ranging from 0º to 360º.

Trick to Remember Trigonometric Table

Let us learn the one-hand trick for remembering the trigonometry table easily! Designate each finger the standard angles as shown in the image. For filling the sine table we will include counting of the fingers, while for the cos table we will simply fill the values in reverse order.

• Step 1: For the sine table, count the fingers on the left side for the standard angle. 
• Step 2: Divide the number of fingers by 4
• Step 3: Take out the square root of the ratio.

Example 1: For sin 0°, there are no fingers on the left-hand side, therefore we will take 0. Dividing the zero by 4 we get 0. Taking the square root of the ratio we would get the value of sin 0° = 0

Example 2: For sin 60°, there are 3 fingers on the left-hand side. Dividing 3 by 4 we get (3/4). Taking the square root of the ratio √(3/4) we would get the value of sin 30° = √3/2.

Similarly, we can find out values for sin 30°, 45°, and 90° to fill the table.

In order to complete the cos table, simply fill in the values of sine in a reverse manner. For tan values, create the ratios by taking numerators of sine and cos values of the corresponding angle as indicated by the arrows in the above picture.

Given below is a list of trigonometric formulas that would help you memorize the trigonometric table, based on the relationship between different trigonometric ratios.

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

• Trigonometry Basics
• Trigonometry Formula
• Trigonometric Identities
• Trig Formulas
• Cosecant Secant and Cotangent Functions
• Trigonometric Ratios

1. Trigonometric values are based on the three major trigonometric ratios: Sine, Cosine, and Tangent. 
   Sine or sin θ = Side opposite to θ / Hypotenuse
   Cosines or cos θ = Adjacent side to θ / Hypotenuse 
   Tangent or tan θ =Side opposite to θ / Adjacent side to θ

2. 0°, 30°, 45°, 60°, and 90° are called the standard angles in trigonometry.

3. The angle values of trigonometric functions cotangent, secant, cosecant, can also be calculated using these standard angles values  of sine, cosecant, tangent.

4. All the higher angle values of trigonometric functions such as 120°, 390°, .... can be easily calculated from the standard angle values.

What Is the Trigonometric Table?

Trigonometric ratios table or sin cos table gives the values of trigonometric functions for the standard angles such as 0°, 30°, 45°, 60°, and 90°, in a tabulated manner. 

What Are the Standard Angles in a Trigonometric Table?

The angles 0°, 30°, 45°, 60°, and 90° are called standard angles, and the trigonometric values for these standard angles are commonly used to solve the trigonometry problems. These values are associated with the measurement of lengths and angles of the right-angle triangle. 

What Does the Infinity Value of the Trigonometric Ratio Mean?

Undefined values are often given an infinity \((\infty )\) value because the value is such large that there is no definite value to assign them at this point. 

What Is Trigonometry?

Trigonometry is the branch of mathematics that deals with the study of the relationship between the sides of a triangle (Right-angled triangle) and its angles.

What Are Trigonometric Functions and their Types?

Trigonometric functions are defined as the functions of an angle of a right-angled triangle. There are 6 basic types of trigonometric functions or ratios which are:

• Sin function
• Cos function
• Tan function
• Cot function
• Cosec function
• Sec function

How to Find the Value of Trigonometric Functions?

All the trigonometric functions are related to the ratios of sides of the triangle and their values can be easily found by using the following relations:

• sinθ = Opposite/Hypotenuse
• cosθ = Adjacent/Hypotenuse
• tanθ = Opposite/Adjacent
• cotθ = 1/tanθ = Adjacent/Opposite
• cosecθ = 1/sinθ = Hypotenuse/Opposite
• secθ = 1/cosθ = Hypotenuse/Adjacent

What Are the Six Basic Trigonometric Functions?

The six basic trigonometric functions are Sine, Cosine, Tan, Sec, Cot, and Cosec function.