Trigonometry Table: Overview, Questions, Preparation

Trigonometry plays an essential role in day-to-day and advanced calculations. Knowing the trigonometric values of some standard angles makes computations faster and easier. That’s where the trigonometry table has a role to play.

A Trigonometric table collectively represents the trigonometric values of standard angles for corresponding trigonometric ratios. The standard angles are 0°,30°,45°,60°,90°. The trigonometric ratios include Sine, Cosine, Tangent, Cotangent, Cosecant, Secant. Values for other angles like 180°,270°, 360°, etc., can also be calculated from the table by correlation between the values. 

The trigonometry table:

Here’s how to tabulate the trigonometric values:

1. Mention all the standard angles in a row, starting from 0 to 360. 
2. Mention all the trigonometric functions in the corresponding column. 
3. Find the sin values for all the angles: Divide 0,1,2,3, and 4 by 4 sequentially and take the square root. For example, sin 0° = √0/4= 0, Sin 30° = √1/4= ½. This will give the values of standard angles between 0 and 90. To find out the values of 180° ,270°, 360°, use the formulae- sin(180° -x) = sinx

                                                  sin(180+x) = -sinx

                                                   sin(360° -x) = -sinx

1. Find the Cos value: Cos values are the opposite of the values of sin angles in the table. Divide 4,3,2,1 and 0 by 4 sequentially and take the square root. You can also use the formula, cos = sin(90° -x)
2. Find tan values: Calculate by the formula tanx= sinx/cosx. For example, if you have to calculate the value of tan30°, then first note, sin 30° = √3/2 and cos 30° = ½, so, tan 30° = sin 30°/cos 30° = √3/2 by ½ = 1/√3.
3. Find the cot, sec and cosec values by using the formulae cotx = 1/tanx,secx = 1/cosx, cosecx = 1/sinx respectively.

Things to remember:

sinx = cos(90°-x) 

cosx = sin(90°-x) 

tanx = cot(90°-x) 

cotx = tan(90°-x) 

secx = cosec(90°-x) 

cosecx = sec(90°-x) 

1/sinx = cosecx

1/cosx = secx

1/tanx = cotx 

The topic is introduced in class X and holds immense significance for the two successive years. In Class X the trigonometric table is limited to acute angles. In Class XI, there is an extension to obtuse angles. Throughout Class X, Class XI, and Class XII, the values remain extremely crucial to solve various questions, be it numerical, proofs, or finding derivative and integral values of trigonometric functions.

• If tan(A+B) = √3 and tan(A-B) = 1/√3, then find the value of A and B, provided both A and B are acute angles. 

From the trigonometry table, we know tan 30° = 1/√3 and tan 60° = √3 

So, comparing those with the question, we can write, 

A+B = 60 ---- equation 1 

A-B = 30 ----equation 2 

Solving equations 1 and 2 we get, 

A= 45° and B = 15° . 

• If tan2A = cot(A-18°), where 2A is an acute angle, find the value of A.

We know that tanx = cot(90°-x) 

=> tan2A = cot(90°-2A)

=> cot(90°-2A) = cot(A-18°) { according to the question}

=> 90°-2A= A-18°

=> 3A= 108°

=> A= 36°

• Evaluate sin 60°cos 30° + sin 30°cos 60°

We know from the trigonometric table that sin 60°= ½, cos 30°= √3/2 sin 30° = √3/2, cos 60°= ½ 

So, putting the values in the question, we get 

½+√3/2 + √3/2+½ 

= 2+2√3/2 

Q: What is Trigonometry?

Q: Why are some trigonometric values for standard angles not defined?

Q: Why are some trigonometric values for obtuse angles negative?

Q: Is a trigonometric table used in real life?

Q: What are the values of sin 0, cos 0, tan 0, cot 0, sec 0, cosec 0?