# Trigonometry formulas for class 10

Trigonometry is a branch of mathematics that deals with angles, lengths and heights of triangles. Trigonometry is applicable in the fields of engineering, astronomy and architectural design. Learning these formulas and applying them can help them attain a better score in mathematics.

We believe that having access to this list of trigonometry formulas for class 10 all in a single page can be really beneficial for the students. Therefore, we have compiled this list and presented it to you through his website. Check this out and download them for reference. Also, make sure to navigate to the other formulas.

 S.no Property Mathematical value 1 sinA$\sin A$ P⁄H$\frac{P}{H}$ 2 cosA$\cos A$ B⁄H$\frac{B}{H}$ 3 tanA$\tan A$ P⁄B$\frac{P}{B}$ 4 cotA$\cot A$ B⁄P$\frac{B}{P}$ 5 cosecA$cosec A$ H⁄P$\frac{H}{P}$ 6 secA H⁄B$\frac{H}{B}$
 S.no Identity Relation 1 tanA$\tan A$ sinA⁄cosA$\frac{\sin A}{\cos A}$ 2 cotA$\cot A$ cosA⁄sinA$\frac{\cos A}{\sin A}$ 3 cosecA$cosec A$ 1⁄sinA$\frac{1}{\sin A}$ 4 secA$\sec A$ 1⁄cosA$\frac{1}{\cos A}$

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# Mensuration formulas class 10

Mensuration is a crucial topic in Geometry. The study of mensuration deals with length, area and volume of different kinds of geometrical shapes.  There are various mensuration formulas for Class 10 students to learn. Learning these formulas and applying them can help them attain a better score in mathematics.

We believe that having access to this list of formulas can be really beneficial for the students. Therefore, we have compiled this list and presented it to you through his website. Check this out and download them for reference. Also, make sure to navigate to the other formulas.

1. Area of rectangle (A) = length(l) × Breath(b)

A = l × b

2. Perimeter of a rectangle (P) = 2 × (Length(l) + Breath(b))

P = 2 × (l + b)

3. Area of a square (A) = Length (l) × Length (l)

A = l × l

4. Perimeter of a square (P) = 4 × Length (l)

P = 4 × l

5. Area of a parallelogram(A) = Length(l) × Height(h)

A = l × h

Parallelogram

6. Perimeter of a parallelogram (P) = 2 × (length(l) + Breadth(b))

P = 2 × (l + b)

7. Area of a triangle (A) = (Base(b) × Height(b)) / 2

A = ½ × b × h

8. Area of triangle(A) = ½ × a × b × ∠ C = ½  b × c × ∠ A = ½ a × c × ∠ B

9. Area of a Circle (A) = πr² = πd²/4

Where r = radius of the circle and d = diameter of the circle.

10. Circumference of a Circle = 2πr = πrd

r= radius of circle

d= diameter of circle

11. Total surface area of cuboid = 2 (lb + bh + lh)

where l= length , b=breadth , h=height

12. Total surface area of cuboid = 6 l²

where l= length

13. Volume of cuboid = l × b × h

14. Volume of cube = l × l × l

15. Area of base of a cone = πr²

16. Curved surface area of a cone = C = π × r × l

Where r = radius of base , l = slanting height of cone

17. Total surface area of a cone = πr (r+l)

18. Volume of right circular cone = 1/3πr²h

Where r = radius of base of cone , h= height of the cone (perpendicular to base)

19. Curved surface area of a cylinder = 2 πrh

Where r = radius of base, h = height of cylinder

20. Total surface area of a cylinder = 2 πr(r + h)

21. Volume of a cylinder = πr²h

22. Surface area of sphere = 4 πr² = πd²

where r= radius of sphere, d= diameter of sphere

23. Volume of a sphere = 4/3 πr³ = 1/6 πd³

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# Basic probability formulas for class 10

Probability in the simplest terms refers to how likely an event is to happen. It is a branch of mathematics which deals with calculating the likelihood of an event’s occurrence. There are formulas for finding out the probability of an event. Learning these formulas and applying them can help them attain a better score in mathematics.

We believe that having access to the list of basic probability formulas for class 10 all in a single page can be really beneficial for the students. Therefore, we have compiled this list and presented it to you through his website. Check this out and download them for reference. Also, make sure to navigate to the other formulas.

## 1. Empirical probability

Empirical probability formula = Probability of an event happening is the ratio of the time similar events happened in the past.

or Empirical probability = Number of times event occurs/Total number of times experiment performed

## 2. Theoretical probability

To understand this, let us consider a random experiment.
Let A be an outcome of the random experiment. Then A is called an event.
The theoretical probability of the event A is given by
P(A) = Number of outcomes favourable to A / Total number of outcomes
Theoretical probability is also known as Classical probability or A Priori probability.

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# Constructions geometry: Circles

This is one of the most important sections for maths in class 10. Learning the formulas given below and applying them can help in getting a better score in mathematics.

We believe that having access to the list of formulas for class 10 all in a single page can be really beneficial for the students. Therefore, we have compiled this list and presented it to you through his website. Check this out and download them for reference. Also, make sure to navigate to the other formulas.

1. Circumference of a circle = 2πr

2. Area of a circle = πr²

3. Length of the arc of the sector of an angle (considering the angle to be x) = x⁄360 2πr

4. Area of the sector of angle (considering the angle to be x) = x/360 πr²

5. Area of segment of a circle = Area of the corresponding sector −  Area of the corresponding triangle

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# Coordinate geometry for class 10

Coordinate geometry is that part of mathematics which provides a connection between algebra and geometry through graphs of lines and curves. There are certain formulas related to coordinate geometry. These formulas are used to find the distance between the two points whose coordinates are given and the area of the triangle formed by three given points. You can also use these formulas to find the coordinates of the point which divides a line segment joining two given points in a given ratio. Learning these formulas and applying them can help students attain a better score in mathematics.

We believe that having access to the list of formulas for coordinate geometry for class 10 on a single page can be really beneficial for students. Therefore, we have compiled this list and presented it to you through this website. Check this out and download the formulas for further reference. Also, make sure to navigate to the other formulas.

## 1. Distance formula

Distance between the points AB is given by D= √(x1-x2)²+(y2-y1)²

Distance of Point A from origin D = √x²+y²

## 2. Section formula

A point P(x,y) which divides the line segment AB in the ratio m1 and m2 is given by x=m1x2+m2x1⁄m1+m2 y=m1y2+m2y1⁄m1+m2

The midpoint P is given by (x1+x2/2), (y1+y2/2)

## 3. Area of triangle

Area of triangle ABC of coordinates A(x1,y1), B(x2,y2) and C(x3,y3)

A=½[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]

For points A, B and C to be collinear, the value of A should be zero.

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# List of geometry formulas for Class 10

Geometry is an important part of Mathematics. There are various formulas to calculate area, base area, lateral area, surface area and perimeter for various geometric shapes. To study geometry, students need to have a clear understanding of various theorems, formulas and properties. Learning these formulas and applying them can help them attain a better score in mathematics.

We believe that having access to the list of geometry formulas for class 10 all in a single page can be really beneficial for the students. Therefore, we have compiled this list and presented it to you through his website. Check this out and download them for reference. Also, make sure to navigate to the other formulas.

## Geometry  Formulas for Class 10

Name Formula
Area of Triangle Area=1basheight$Area = \frac{1}{2} base \cdot height$
Pythagorean Theorem a2+b2=c2$a^{2} + b^{2} = c^{2}$
Area of a Circle Area=πr2$Area = \pi r^{2}$
Circumference of a Circle C=2πr$C = 2\pi r$ or πd$\pi d$
Area of a Parallelogram Area=basheight$Area = base \cdot height$
Area of a Trapezoid Area={(base1+base2)2}×height$Area =\frac{base_{1}+base_{2}}{2}\cdot height$
Area of a Kite or a Rhombus Area=½×diagonaldiagonal2$Area = \frac{1}{2} diagonal_{1}\cdot diagonal_{2}$
Area of a Square Area=side2$Area = side^{2}$
Area of a Regular Polygon Area=½×perimeteapothem$Area = \frac{1}{2}perimeter\cdot apothem$
Number of Diagonal in n-sided Polygon Diagonals=n(n3)⁄2$Diagonals = \frac{n \left (n-3 \right )}{2}$
Slope m=y2y1⁄x2x1$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}$
Midpoint Formula (xmp,ymp)=[(x1+x2)⁄2],[(y1+y2)⁄2]$\left ( x_{mp},y_{mp} \right )=\left ( \frac{x_{1}+x_{2}}{2} \right ),\left ( \frac{y_{1}+y_{2}}{2} \right )$
Distance Formula d=(x2x1)2+(y2y1)2$d=\sqrt{\left ( x_{2}-x_{1} \right )^{2}+\left ( y_{2}-y_{1} \right )^{2}}$
Equation of a Circle (xh)2+(yk)2=r2$\left ( x-h \right )^{2}+\left ( y-k \right )^{2}=r^{2}$<

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# List of Algebra Formulas

Algebra is an integral part of Mathematics. It uses symbols and letters to represent quantities and numbers in equations and formulae. The two basic types of algebra are Elementary algebra and Modern algebra. To study algebra students need to have a clear understanding of various formulas, terms and concepts. Learning these formulas and applying them can help them attain a better score in mathematics.

We believe that having access to the list of algebra formulas for class 10 all in a single page can be really beneficial for the students. Therefore, we have compiled this list and presented it to you through his website. Check this out and download them for reference. Also, make sure to navigate to the other formulas.

## Algebraic Identities For Class 10

(a+b)2$\mathbf{(a+b)^{2}}$ =a2+2ab+b2$=a^2+2ab+b^{2}$
(ab)2$\mathbf{(a-b)^{2}}$ =a22ab+b2$=a^{2}-2ab+b^{2}$
(a+b)(ab)$\mathbf{\left (a + b \right ) \left (a – b \right ) }$ =a2b2$= a^{2} – b^{2}$
(x+a)(x+b)$\mathbf{ \left (x + a \right )\left (x + b \right ) }$ =x2+(a+b)x+ab$= x^{2} + \left (a + b \right )x + ab$
(x+a)(xb)$\mathbf{\left (x + a \right )\left (x – b \right ) }$ =x2+(ab)xab$= x^{2} + \left (a – b \right )x – ab$
(xa)(x+b)$\mathbf{\left (x – a \right )\left (x + b \right )}$ =x2+(ba)xab$= x^{2} + \left (b – a \right )x – ab$
(xa)(xb)$\mathbf{\left (x – a \right )\left (x – b \right ) }$ =x2(a+b)x+ab$= x^{2} – \left (a + b \right )x + ab$
(a+b)3$\mathbf{\left (a + b \right )^{3}}$ =a3+b3+3ab(a+b)$= a^{3} + b^{3} + 3ab\left (a + b \right )$
(ab)3$\mathbf{\left (a – b \right )^{3} }$ =a3b33ab(ab)$= a^{3} – b^{3} – 3ab\left (a – b \right )$
(x+y+z)2$\mathbf{(x + y + z)^{2}}$ =x2+y2+z2+2xy+2yz+2xz$= x^{2} + y^{2} + z^{2} + 2xy + 2yz + 2xz$
(x+yz)2$\mathbf{(x + y – z)^{2}}$ =x2+y2+z2+2xy2yz2xz$= x^{2} + y^{2} + z^{2} + 2xy – 2yz – 2xz$
(xy+z)2$\mathbf{(x – y + z)^{2} }$ =x2+y2+z22xy2yz+2xz$= x^{2} + y^{2} + z^{2} – 2xy – 2yz + 2xz$
(xyz)2$\mathbf{(x – y – z)^{2}}$ =x2+y2+z22xy+2yz2xz$= x^{2} + y^{2} + z^{2} – 2xy + 2yz – 2xz$
x3+y3+z33xyz$\mathbf{x^{3} + y^{3} + z^{3} – 3xyz }$ =(x+y+z)(x2+y2+z2xyyzxz)$= (x + y + z)(x^{2} + y^{2} + z^{2} – xy – yz -xz)$
x2+y2$\mathbf{x^{2} + y^{2}}$ =12[(x+y)2+(xy)2]$= \frac{1}{2} \left [(x + y)^{2} + (x – y)^{2} \right ]$
(x+a)(x+b)(x+c)$\mathbf{(x + a) (x + b) (x + c) }$ =x3+(a+b+c)x2+(ab+bc+ca)x+abc$= x^{3} + (a + b +c)x^{2} + (ab + bc + ca)x + abc$
x3+y3$\mathbf{x^{3} + y^{3}}$ =(x+y)(x2xy+y2)$= (x + y) (x^{2} – xy + y^{2})$
x3y3$\mathbf{x^{3} – y^{3}}$ =(xy)(x2+xy+y2)$= (x – y) (x^{2} + xy + y^{2})$
x2+y2+z2xyyzzx$\mathbf{x^{2} + y^{2} + z^{2} -xy – yz – zx }$ =12[(xy)2+(yz)2+(zx)2]$= \frac{1}{2} [(x-y)^{2} + (y-z)^{2} + (z-x)^{2}]$

## Linear Equation in Two Variables

a1x+b1y+c1$\mathbf{a_{1}x + b_{1}y + c_{1} }$ =0$= 0$
a2x+b2y+c2$\mathbf{a_{2}x+ b_{2}y + c_{2}}$ =0$= 0$

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