can someone give me a perfect trigonometry table for 10 class
Answers
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
The trigonometric ratios of a triangle are also called the trigonometric functions. Sine, cosine, and tangent are 3 important trigonometric functions and are abbreviated as sin, cos and tan. Let us see how are these ratios or functions, evaluated in case of a right-angled triangle.
Consider a right-angled triangle, where the longest side is called the hypotenuse, and the sides opposite to the hypotenuse are referred to as the adjacent and opposite sides.
Trigonometry Ratios
Six Important Trigonometric Functions
The six important trigonometric functions (trigonometric ratios) are calculated using the below formulas and considering the above figure. It is necessary to get knowledge about the sides of the right triangle because it defines the set of important trigonometric functions.
Functions Abbreviation Relationship to sides of a right triangle
Sine Function sin Opposite side/ Hypotenuse
Tangent Function tan Opposite side / Adjacent side
Cosine Function cos Adjacent side / Hypotenuse
Cosecant Function cosec Hypotenuse / Opposite side
Secant Function sec Hypotenuse / Adjacent side
Cotangent Function cot Adjacent side / Opposite side
Trigonometry Angles
The trigonometry angles which are commonly used in trigonometry problems are 0°, 30°, 45°, 60° and 90°. The trigonometric ratios such as sine, cosine and tangent of these angles are easy to memorize. We will also show the table where all the ratios and their respective angle’s values are mentioned. To find these angles we have to draw a right-angled triangle, in which one of the acute angles will be the corresponding trigonometry angle. These angles will be defined with respect to the ratio associated with it.
For example, in a right-angled triangle,
Sin θ = Perpendicular/Hypotenuse
or θ = sin-1 (P/H)
Similarly,
θ = cos-1 (Base/Hypotenuse)
θ = tan-1 (Perpendicular/Base)
Trigonometry Table
Check the table for common angles which are used to solve many trigonometric problems involving trigonometric ratios.
Angles 0° 30° 45° 60° 90°
Sin θ 0 ½ 1/√2 √3/2 1
Cos θ 1 √3/2 1/√2 ½ 0
Tan θ 0 1/√3 1 √3 ∞
Cosec θ ∞ 2 √2 2/√3 1
Sec θ 1 2/√3 √2 2 ∞
Cot θ ∞ √3 1 1/√3 0
In the same way, we can find the trigonometric ratio values for angles beyond 90 degrees, such as 180°, 270° and 360°.
Unit Circle
The concept of unit circle helps us to measure the angles of cos, sin and tan directly since the centre of the circle is located at the origin and radius is 1. Consider theta be an angle then,
Trigonometry 2
Suppose the length of the perpendicular is y and of base is x. The length of the hypotenuse is equal to the radius of the unit circle, which is 1. Therefore, we can write the trigonometry ratios as;
Sin θ y/1 = y
Cos θ x/1 = x
Tan θ y/x
List of Trigonometry Formulas
The Trigonometric formulas or Identities are the equations which are true in the case of Right-Angled Triangles. Some of the special trigonometric identities are given below –
Pythagorean Identities