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.
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.
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.
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
