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1. TRIGONOMETRY FOR CLASS 10
K.j.Kailesh class 10

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

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