In this Mathematic tutorial, we will study all 6 functions of trigonometry. The trigonometry table represents these functions with angles in degrees and radians. Below are some of the values and formulae for radians, pi, and degrees.

Pi ( \pi)= \frac{22}{7}= 3.141592…(approximately)

Degree = Radian * 180 / pi (the degree to radian conversion)
Radian = Degree * pi / 180 (radian to degree conversion)

What is a trigonometry table?

The trigonometric table is a collection of various functions like sin, cos, etc. with standard angles including 0°, 30°,45°, 60°,90°,180°,270°, and 360°.

Firstly, trigonometry deals with the relation between the sides of the right-angled triangle and its angle. The trigonometry ratio tables consist of sine, cosine, tangent, secant, cosecant, and cotangent.

Trigonometry table with triangle side names

Secondly, this table might seem complex but can easily be learned by simply remembering the sine values for 8 standard angles.

Finally, using the trigonometry formula you can easily solve any complex trigonometric problem.

We will cover the concept of the trigonometric table along with the trigonometry formula with a few examples to get a better understanding of this concept.

Trigonometry Values Table

The below table represents the standard values for a trigonometric function.

Angles (Degree)Angles (Radians)sincostancotcosecsec
0°0°010∞∞1
30°π/61/2√3/21/√3√322/√3
45°π/41/√21/√211√2√2
60°π/3√3/21/2√31/√32/√32
90°π/210∞01∞
180°π0-10∞∞-1
270°3π/2-10∞0-1∞
360°2π010∞∞1

 

Likewise, we can get values for cot, sec and cse using the following formulas:
\csc\theta =\frac{1}{\sin\theta}\\ \sec\theta =\frac{1}{\cos\theta}\\ \tan\theta =\frac{1}{\cot\theta}\\ \tan\theta =\frac{\sin}{\cos \theta}\\ \sin (180° − \theta) = \sin \theta\\ \sin (180° + \theta) = -\sin \theta\\ \sin (360° − \theta) = -\sin \theta\\

Trigonometry tables have wide applications in various fields like science, engineering, Marine biology, navigation and many more.

Few solved examples using trigonometry formulas

Example 1: Consider a right \triangle ABC , \angle B. The length of the base, AB = 10 cm and the length of perpendicular BC =5 cm. Find the value of sin A?

Solution:

The base of a right-angled triangle = AB = 6 cm

Perpendicular of a right-angled triangle BC = 8 cm

By Pythagoras Theorem

(Hypotenuse)²=(Base)²+(Perpendicular)²

H² = 6²+8²

= 36+64

= 100

H² = 10²

H = 10

Therefore, 10 cm is the length of the third side.

So, The Angle \sin A =\frac{Perpendicular}{Hypotenuse} \sin A =\frac{ 10}{8}

As a result, The values of \sin A is \frac{10}{8}.

Example 2: Prove that \frac{\sin(x-y)}{\sin(x+y)}=\frac{\tan x- \tan y}{\tan x+\tan y}\\ using trigonometry formulas

Solution:

LHS=\frac{\sin(x-y)}{\sin(x+y)}=\frac{\sin x\cos y-\cos x \sin y}{\sin x\cos y+\cos x \sin y}\\ Dividing numerator and denominator by \cos x \cos y \\ We have,
=\frac{\frac{\sin x\cos y}{\cos x \cos y}-\frac{\cos x \sin y}{{\cos x \cos y}}}{\frac{\sin x\cos y}{{\cos x \cos y}}+\frac{\cos x \sin y}{{\cos x \cos y}}} \\       (Using addition and subtraction formula)

=\frac{\frac{\sin x}{\cos x }-\frac{ \sin y}{{ \cos y}}}{\frac{\sin x}{{\cos x }}+\frac{ \sin y}{{\cos y}}} \\ =\frac{ \tan x -\tan y}{ \tan x +\tan y}= RHS

Hence, LHS= RHS

 

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