Trigonometry Table

Trigonometry Table

Trigonometry Table is a standard table that helps us find the values of trigonometric ratios for standard angles such as 0^o, 30^o, 45^o, 60^o and 90^o. It consists of all six trigonometric ratios: sine, cosine, tangent, cosecant, secant, and cotangent. Trigonometry tables are widely used by students, engineers and scientists. It is also used for surveying, astronomy and navigation.

A trigonometry table for standard angles and some non-standard angles:

Trigonometric Values

The term "trigonometric value" refers to the values of various ratios in trigonometry. All trigonometric ratios are related to the sides of a right-angled triangle and can be determined using the following ratios.

How to Remember Trigonometry Table?

The trigonometry table is simple to learn and will be helpful in a variety of ways. It is quite easy to memorise the trigonometry table if you are familiar with the trigonometric formulae. The trigonometry formulae are a prerequisite for creating a Trigonometry table. The formulas are given below:

How to Create a Trigonometric Table?

The steps to create a trigonometric table are given below:

Step 1: Create a table with the top row listing the angles such as 0^o, 30^o, 45^o, 60^o and 90^o and write all trigonometric functions in the first column, such as sin, cos, tan, cosec, sec and cot.

Step 2: Write the values of sin for 0^o, 30^o, 45^o, 60^o and 90^o angles as 0, $\frac{\frac{1}{}}{\frac{2}{}}$, $\frac{\frac{1}{}}{\sqrt{2}}$ ,$\frac{\frac{\sqrt{3}}{}}{2}$ and 1 respectively, in the second row of the table as shown below:

Step 3: To write the values of cos, just write the above row in the opposite manner, which means the value of sin 90^o is the same as that of cos 0^o.

Step 4: Determining the value of tan is really easy because we know tan x = sin x/cos x. For example, if we want to find the value of tan 30^o, then just divide the value of sin 30^o by cos 30^o. So, tan 30^o = $\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}$ = $\frac{\frac{1}{}}{\sqrt{3}}.$

Hence, the value of the tan function can be determined as:

Step 5: Let’s determine the value of cot x using the relationship: cot x = $\frac{\frac{1}{}}{\frac{\mathrm{tan\; x}}{}}$.

To find the value of cot 30^o, just take the reciprocal of tan 30^o, which will be √3.

Now, Use this relation to generate the cot function.

Step 6: Now we will determine the value of cosec x using the relation: cosec x = $\frac{\frac{1}{}}{\frac{\mathrm{Sin\; x}}{}}$.
Cosec x is the reciprocal of sin x.

Step 7: It’s time to determine the value of the last trigonometric function, which is sec x using the relation: sec x = $\frac{\frac{1}{}}{\frac{\mathrm{Cos\; x}}{}}$

If we follow the above steps, we can easily remember the trigonometric table.

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Solved Examples

Example 1: Using the trigonometric table, evaluate:

Solution: As we know, sin 90^o = 1 and cos 30^o = $\frac{\sqrt{3}}{2}$. Substituting the above values in the given expression, we will get:

= 1² + (√3 / 2)² = 1 + $\frac{\frac{3}{}}{\frac{4}{}}$ = $\frac{\frac{7}{}}{\frac{4}{}}$.
Hence, the final answer will be $\frac{\frac{7}{}}{\frac{4}{}}$.

Example 2: Find the value of sin 30^o + (tan 45^o x cosec 30^o).

Solution: Substituting the values of sin 30^o, tan 45^o and cosec 30^o in the given expression, we will get:
sin 30^o+ (tan 45^o x cosec 30^o) = $\frac{\frac{1}{}}{\frac{2}{}}$ + 1 x 2 = $\frac{\frac{1}{}}{\frac{2}{}}$ + 2 = $\frac{\frac{5}{}}{\frac{2}{}}$
Hence, the final answer will be $\frac{\frac{5}{}}{\frac{2}{}}$.

Frequently Asked Questions

1. What is a trigonometry table?

Answer: A trigonometry table is a reference table used in mathematics to find the values of trigonometric functions like sine, cosine, and tangent for different angles.

2. What are the uses of trigonometry tables?

Answer: Trigonometry is widely used in various fields. To calculate complex problems in trigonometry, we need to know the values of trigonometric functions. That's where the trigonometry table comes into play. Trigonometry tables make complicated computations simpler. When dealing with trigonometric functions, they are useful tools for scientists, engineers and students.

3. What angles are covered in a trigonometry table?

Answer: Trigonometry tables cover angles ranging from 0 to 90 degrees or 0 to 360 degrees, depending on the table's format.

4. Do we still need trigonometry tables these days?

Answer: Even though we have digital tools and calculators now, people still use trigonometry tables in schools and jobs to check things and make sure they're right. They're like a handy guidebook for math problems!