Trigonometry, derived from Greek terms meaning 'three angles' and 'measure', focuses on the relationships between the sides and angles of triangles, especially right-angled triangles. The document explains key concepts such as the Pythagorean theorem and provides formulas for calculating trigonometric functions (sine, cosine, tangent, etc.) based on the triangle's dimensions. Additionally, it highlights practical applications of trigonometry, including measuring inaccessible lengths and constructing tables for trigonometric functions.

1. TRIGONOMETRY FOR CLASS 10
BY-SUDHANSHU SABHARWAL
B.TECH(CIVIL ENGINEERING) 2015

2. TRIGONOMETRY
• Trigonometry is derived from Greek words
trigonon(three angles) and metron (measure).
• Trigonometry is the branch of mathematics which
deals with triangles, particularly triangles in a plane
where one angle of the triangle is 90 Degree.
• Trigonometry specifically deals with relationships
between the sides and the angles of a triangle, i.e.
on the trigonometric functions, and with
calculations based on these functions.

3. Right Triangle
• A triangle in which one angle is equal to 90 degree is
called a right angled triangle.
• The side opposite to the right angle is known as
hypotenuse.
• AC is the hypotenuse
• The other two sides are known as legs or base and
altitude
• AB and AC are base and altitude respectively

4. RIGHT ANGLE

5. Pythagoras Theorem
• In any right triangle, the area of the square whose
side is the hypotenuse is equal to the sum of the areas
of the squares whose sides are the two legs.
• In the figure,
• AC2
= AB2
+ BC2

6. Pythagoras theorem
example
AC2
+BC2
=AB2
AC=4,BC=3

7. WHY
TRIGONOMETRY
• See in Pythagoras theorem we have given two
sides and using theorem formula we can find
the third side
• But in few questions we know the dimension
of one side only and we find other two sides
using trigonometry

8. SURVEYING

9. Value for Trigonometric Functions for Angle C
• Sinθ = AB/AC
• Cos θ = BC/AC
• Tanθ = AB/BC
• Cosecθ = AC/AB
• Secθ = AC/BC
• Cotθ = AC/AB

11. APPLICATIONS
• Measuring inaccessible lengths
• Height of a building (tree, tower, etc.)
• Width of a river (canyon, etc.)

12. HOW TO MAKE A TABLE OF TRIGONOMETRIC
FUNCTIONS
• FIRSTLY WRITE DOWN THE FUCTIONS ON LEFT
SIDE - SIN,COT,TAN,COSEC,SEC,COT
• THEN WRITE DOWN THE ANGLES ON THE TOP
0,30,45,60,90 DEGREE
• THEN WRITE STARTING FROM THE ZERO
DEGREE TO 90 – 0,1,2,3,4 AND DIVIDE THEM
BY 4 AND TAKE SQUARE ROOT OF THEM

13. CONTINUE
• THE VALUES WE OBTAINTED FROM THIS ARE
THE VALUES OF SIN
• THEN FOR COS WRITE DOWN THE VALUES OF
SIN FROM ORDER 90,60,45,30,0
• LIKE SIN 90= COS 0, SIN 60=COS 30, SIN 45=
COS 45, SIN 30= COS 60,SIN 0= COS 90
• NOW TAN= SIN/COS SO WE DIVIDE THE
VALUES OF ANGLES FOR THE TAN

14. CONTINUE
• WHEN 0 COMES IN THE DENOMINATOR THE
FRACTION BECOMES INFINTY ∞
• FOR COSEC= 1/ SIN SO WE REVERSE THE
VALUES OF SIN FOR THIS
• FOR SEC=1/COS SO WE REVERSE THE VALUES
OF COS FOR THIS
• FOR COT=1/TAN SO WE REVERSE THE VALUES
OF TAN FOR THIS