Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. It emerged from applications of geometry to astronomy in ancient Greece. The word trigonometry comes from Greek words meaning "three", "sides", and "measure". Trigonometry defines ratios between the sides and angles of right triangles, and establishes trigonometric identities that are true for all angle values. These identities relate trigonometric functions of complementary angles and derive important equations like the Pythagorean identity.

4. Trigonometry is a branch of mathematics that studies
relationships involving lengths and angles of triangles. The field
emerged in the Hellenistic world during the 3rd century BC from
applications of geometry to astronomical studies.
The word ‘trigonometry’ is derived from the Greek word ‘tri’
(meaning three), ‘gon’ (meaning sides) and ‘metron’ (meaning
measure).

5. Trigonometry is a branch
of mathematics that
studies triangles and the relationships
between their sides and the angles
between these sides.

7. Side
Opposite
To Angle A
HYPOTENUSE
Side Adjacent
To Angle A
ө
A
B
C
AB = HYPOTENUSE
BC = SIDE ADJACENT TO ANGLE A
AC = SIDE OPPOSITE TO ANGLE A

8. TRIGONOMETRIC RATIOS ABBREVIATIONS
SINE SIN
COSINE COS
TANGENT TAN
COSECANT CSC OR COSEC
SECANT SEC
COTANGENT COT

9. Side Opposite
To Angle A
HYPOTENUSE
Side Adjacent
To Angle A
ө
A
B
C
THE TRIGONOMETRIC RATIOS of
the angle A in right triangle ABC are
defined as follows :

10. ө 0 30 45 60 90
sin ө 0 1
cos ө 1 0
tan ө 0 1 Not
Defined
csc ө Not
Defined
2 1
sec ө 1 2 Not
Defined
cot ө Not
Defined
1 0
2
1
2
1
2
3
3
2
3
1
3
1
2
1
2
1
1
3
1
3
2
3
3
2
1
2
1
2

11. SIN (90 - A) = COS A
COS (90 - A) = SIN A
TAN (90 - A) = COT A
COT (90 - A) = TAN A
SEC (90 - A) = COSEC A
COSEC (90 - A) = SEC A

12. sin2 u + cos2 u = 1
1 + tan2 u = sec2 u
1 + cot2 u = csc2 u
We know,
An equation is called an identity when it is true
for all the values of the variable involved .
Similarly, an equation involving trigonometric
ratios of an angle is called TRIGONOMETRIC
IDENTITIES.

15. Line of
Sight
Horizontal

16. The angle which the line of
sight makes with a horizontal
line drawn away from their
eyes is called the angle of
Elevation of aero plane from
them.

17. Angle of
Elevation
Angle of
Elevation

18. If the pilot of the aero plane
looks downwards at any object
on the ground then the Angle
between his line of sight and
horizontal line drawn away
from his eyes is called Angle of
Depression

19. Angle of
Depression
Horizontal
Angle of
Depression

21. Thank You