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. It has a vast number of applications in other fields of Mathematics. Many geometric calculations can be easily figured out using the table of trigonometric functions and formulas as well.

Trigonometric 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 trigonometric ratios of standard angles are essential to solve the trigonometry problems. Therefore, it is necessary to remember the values of the trigonometric 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 the Fast Fourier Transform (FFT) algorithms.

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 then remembering the trigonometry table is very easy. The Trigonometry ratios table is dependent upon the trigonometry formulas.

Below are the few steps to memorize the trigonometry table.

Before beginning, try to 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 = cosec (90° – x)
• cosec x = sec (90° – x)
• 1/sin x = cosec x
• 1/cos x = sec x
• 1/tan x = cot x

Steps to Create a 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 functions in the first column such as sin, cos, tan, cosec, sec, cot.

Step 2: Determine the value of sin

To determine the values of sin, divide 0, 1, 2, 3, 4 by 4 under the root, respectively. See the example below.

To determine the value of sin 0°

Step 3: Determine the value of cos

The cos-value is the opposite angle of the sin angle. To determine the value of cos divide by 4 in the opposite sequence of sin. For example, divide 4 by 4 under the root to get the value of cos 0°. See the example below.

To determine the value of cos 0°

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 at 0° divide the value of sin at 0° by the value of cos at 0°. See the example below.

tan 0°= 0/1 = 0

Similarly, the table would be.

Step 5: Determine the value of cot

The value of cot is equal to the reciprocal of tan. The value of cot at 0° will obtain by dividing 1 by the value of tan at 0°. So the value will be:

cot 0° = 1/0 = Infinite or Not Defined

Same way, the table for a cot is given below.

Step 6: Determine the value of cosec

The value of cosec at 0° is the reciprocal of sin at 0°.

cosec 0°= 1/0 = Infinite or Not Defined

Same way, the table for cosec is given below.

Step 7: Determine the value of sec

The value of sec can be determined by all reciprocal values of cos. The value of sec on 0° is the opposite of cos on 0°. So the value will be:

In the same way, the table for sec is given below.

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Solved Examples

Example 1:

Find the value of tan 45^o + 2 cos 60^o – sec 60^o.

Solution:

From the trigonometry table, tan 45^o = 1, cos 60^o = ½ and sec 60^o = 2

Therefore, tan 45^o + 2 cos 60^o – sec 60^o = 1 + 2 × ½ – 2 = 1 + 1 – 2 = 0

Example 2:

Find the value of sin 75^o.

Solution:

We can write,

sin 75^o = sin (45^o + 30^o) = sin 45^o cos 30^o + cos 45^o sin 30^o 

{since, sin (A + B) = sin A cos B + cos A sin B}

= 1/√2 × √3/2 + 1/√2 × 1/2 = (√3 + 1)/2√2

∴ sin 75^o= (√3 + 1)/2√2

Example 3:

Using the trigonometric table, evaluate sin² 30^o + cos²30^o.

Solution:

By the trigonometric identities, we know that sin² 𝜃 + cos² 𝜃 = 1. But let us prove this using the trigonometric table.  

sin² 30^o + cos²30^o = (½)² + (√3/2)² = ¼ + ¾ = 4/4 = 1

Practice Questions

1. Find the value of tan 45^o + sec 30^o cos 30^o.
2. Find the value of tan 15^o.
3. Verify tan 2A = (2 tan A)/(1 – tan² A) for A = 30^o.