small introduction on trignomentry for class 10

1. PROJECT ON
TRIGONOMETRY
DESIGNED BY:
AARTHEE A
AMIRTHA VARSHINI V
HARINI R
HEMA M
SUKEERTHI S

2. TRIGONOMETRIC RATIOS
Let us take a right angle ABC
as shown in figure.
Here, ∟CAB or ∟A is an
acute angle. Note the position
of side BC with respect to
∟A. It faces ∟A. we call it
the side opposite to
∟A(perpendicular). AC is
hypotenuse of the right angle
and the side AB is a part of
∟A. so, we call it the side
adjacent to ∟A(base).

3. The trigonometric ratios of the angle A in the right triangle
ABC see in fig.
•Sin of A =side opposite to angle A =BC
hypotenuse AC
•Cosine of A =side adjacent to angle A =AB
hypotenuse AC
•Tangent of A =side opposite to angle A =BC
side adjacent to angle A AB
C
A B

4. Cosecant of A = 1 = hypotenuse = AC
sin of A side opposite to angle A BC
Secant of A = 1 = hypotenuse = AC
sin of A side adjacent to angle a AB
Cotangent of A= 1 =side adjacent to angle A= AB
tangent of A side opposite to angle A BC
C
A B

5. RECIPROCALS OF SIN , COS &
TAN
Sin θ = reciprocal= Cosec θ
Cos θ = reciprocal = Sec θ
Tan θ = reciprocal = Cot θ
Means :-
Sin θ = 1/ Cosec θ
(sin θ * cosec θ = 1 )
Cos θ = 1/ Sec θ
( cos θ * sec θ = 1 )
Tan θ = 1/ Cot θ
( tan θ * cot θ = 1 )

6. VALUES OF TRIGONOMETRIC RATIOS
∟θ 0° 30° 45° 60° 90°
Sin θ 0 1/2 1/√2 √3/2 1
Cos θ 1 √3/2 1/√2 1/2 0
Tan θ 0 1/√3 1 √3 NOT
DEFINED
Cosec
θ
NOT
DEFINED 2 √2 2/√3 1
Sec θ 1 2/√3 √2 2 NOT
DEFINED
Cot θ NOT
DEFINED √3 1 1/√3 0

7. FORMULAS
Sin ( 90° – θ ) = Cos θ
Cos ( 90° – θ ) = Sin θ
Tan ( 90° – θ ) = Cot θ
Cot ( 90° – θ ) = Tan θ
Cosec ( 90° – θ ) = Sec
θ
Sec ( 90° – θ ) = Cosec

8. MAIN IDENTITIES
Sin²θ + Cos² θ = 1
1 + Tan² θ = Sec² θ
1 + Cot² θ = Cosec² θ
Sinθ / Cos θ = Tan θ
Cosθ / Sin θ = Cot θ
Sin² θ / Cos² θ = Tan² θ
Cos² θ / Sin² θ = Cot² θ

9. STEPS OF PROVING THE
IDENTITIES
1) Solve the left hand side or right hand
side of the identity.
2) Use an identity if required.
3) Use formulas if required.
4) Convert the terms in the form of sinθ
or cos θ according to the question.
5) Divide or multiply the L.H.S. by sin θ or
cos θ if required.
6) Then solve the R.H.S. if required.
7) Lastly , verify that if L.H.S. = R.H.S.

10. THANK
YOU