Trigonometry Formulas for Class 10 Maths

Here we are providing trigonometry formulas for class 10 maths.

Students are suggested to remember these formulas so that there won’t be any problem in solving questions related to trigonometry.

Trigonometry formulas Class 10 are related to the relationships between the sides and angles of a right-angled triangle. Trigonometric ratios are ratios of sides of the right triangle. These formulas are quite important to find the angles and the length of sides by applying trigonometric ratios.

Apart from mathematics, class 10 trigonometry formulas hold great significance in various subjects like architecture, engineering, astronomy, geography, music, electronics, civil engineering, oceanography, image compression, chemistry and medical imaging. Read along to know more about important class 10 trigonometry formulas, their practical applications and their importance.

Trigonometry Formulas for Class 10 Maths

Trigonometric Ratios (T-RATIOS) of an Acute Angle of a Right Triangle

(i) $$ {sine}\, \theta=\frac{\text { perpendicular }}{\text { hypotenuse }}=\frac{y}{r}$$ Note: It is written as .
(ii) $${cosine}\, \theta=\frac{\text { base }}{\text { hypotenuse }}=\frac{x}{r}$$ Note: It is written as .
(iii) $$tangent\, \theta=\frac{\text { perpendicular }}{\text { base }}=\frac{y}{x}$$ Note: it is written as .
(iv) $${cosecant}\, \theta=\frac{\text { hypotenuse }}{\text { perpendicular }}=\frac{r}{y}$$ Note: It is written as .
(v) $${secant} \theta=\frac{\text { hypotenuse }}{\text { base }}=\frac{r}{x}$$ Note: It is written as .
(vi) $$cotangent\, \theta=\frac{\text { base }}{\text { perpendicular }}=\frac{x}{y}$$ Note: It is written as .

RECIPROCAL RELATION

$$(i) \,cosec \theta=\frac{1}{\sin \theta}$$
$$(ii) \,\sec \theta=\frac{1}{\cos \theta}$$
$$(iii)\, \cot \theta=\frac{1}{\tan \theta}$$

POWER OF T-RATIOS

$$
(\sin \theta)^2=\sin ^2 \theta ; \quad(\sin \theta)^3=\sin ^3 \theta ; \quad(\cos \theta)^3=\cos ^3 \theta
$$

QUOTIENT RELATION OF T-RATIOS

$$(i) \,\tan \theta=\frac{\sin \theta}{\cos \theta}$$
$$(ii) \, \cot \theta=\frac{\cos \theta}{\sin \theta}$$
$$(iii)\, \tan \theta \cdot \cot \theta=1$$

Square Relation or Trigonometric Identities

$$(i) \,\sin ^2 \theta+\cos ^2 \theta=1$$
$$(ii) \,1+\tan ^2 \theta=\sec ^2 \theta$$
$$(iii) \,1+\cot ^2 \theta={cosec} ^2 \theta$$

TABLE FOR T-RATIOS

TRIGONOMETRIC RATIOS OF COMPLEMENTARY ANGLES

$$(i)\,\sin \left(90^{\circ}-\theta\right)=\cos \theta$$
$$(ii)\,\cos \left(90^{\circ}-\theta\right)=\sin \theta$$
$$(iii)\,\tan \left(90^{\circ}-\theta\right)=\cot \theta$$
$$(iv) \,\cot \left(90^{\circ}-\theta\right)=\tan \theta$$
$$(v) \,\sec \left(90^{\circ}-\theta\right)={cosec} \theta$$
$$(vi)\,{cosec}\left(90^{\circ}-\theta\right)=\sec \theta$$

What is Trigonometry?

Trigonometry is a branch of mathematics that deals with the study of the relationships between the angles and sides of triangles, especially right-angled triangles. The word “trigonometry” is derived from two Greek words: “trigonon” (meaning triangle) and “metron” (meaning measure). It has applications in various fields, including physics, engineering, astronomy, surveying, and architecture.

Key aspects of trigonometry include:

1. Trigonometric Ratios: Trigonometry revolves around trigonometric ratios, which are ratios of the lengths of the sides of a right-angled triangle. The main trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These ratios help relate angles to the lengths of the sides.
2. Right-Angled Triangles: In trigonometry, right-angled triangles hold significant importance. These triangles have one angle of 90 degrees, and the other two angles are acute (less than 90 degrees). The side opposite the right angle is called the hypotenuse, while the other two sides are called the legs.

Trigonometry plays a crucial role in many scientific and engineering disciplines, helping us understand and model various natural phenomena and enabling accurate calculations and measurements in practical applications.

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