a powerpoint presentation on triginometry

1. Made by:
BHAVUN CHHABRA
10TH - B

2.  Trigonometry is the study and solution of
Triangles. Solving a triangle means finding
the value of each of its sides and angles.
The following terminology and tactics will be
important in the solving of triangles.
Pythagorean Theorem (a2+b2=c2). Only for right angle
triangles
Sine (sin), Cosecant (csc or sin-1)
Cosine (cos), Secant (sec or cos-1)
Tangent (tan), Cotangent (cot or tan-1)
Right/Oblique triangle

3. us e
 Since a triangle has three
ten
sides, there are six ways to
adjacent
o
divide the lengths of the
hyp
sides
 Each of these six ratios has
a name (and an
abbreviation)  The ratios depend on the
 Three ratios are most used: shape of the triangle (the
opposite
 sine = sin = opp / hyp
 cosine = cos = adj / hyp angles) but not on the size
 tangent = tan = opp / adj
e
The other three ratios are
nus

ote
adjacent
 cosecant= cosec= hyp/ opp
hyp
 secant= sec= hyp/ adj
 cotangent = cot = adj/opp
opposite

5. THE SIDE OPPOSITE TO THE ANGLE
angle
opposite
opposite
opposite
angle angle
angle
opposite
OP
PO
SIT
E SID
E

6. THE SIDE ADJACENT TO THE ANGLE
angle
angle angle
adjacent
angle
t nec a da
t nec a da
j
j
ADJACENT

7. THE LONGEST SIDE
se
enu
hy pot e h yp
e nus ote
nu
hy pot se
hyp
o te n
use
HY
PO
TE
NU
SE

8. THREE TYPES TRIGONOMETRIC
RATIOS
There are 3 kinds of trigonometric ratios
we will learn.
sine ratio
cosine ratio
tangent ratio

9. sine ratio
θ
For any right-angled triangle
Opposite side
Sinθ =
hypotenuses

10. θ
For any right-angled triangle
Adjacent Side
Cosθ =
hypotenuses

11. θ
For any right-angled triangle
Opposite Side
tanθ =
Adjacent Side

13. Reciprocal Identities
1 1 1
cot θ = secθ = cscθ =
tan θ cosθ sin θ
Quotient Identities
sin θ cosθ
tan θ = cot θ =
cosθ sin θ
Pythagorean Identities
sin θ + cos θ = 1 tan θ + 1 = sec θ 1 + cot θ = csc θ
2 2 2 2 2 2
Negative-Number Identities
sin( −θ ) = − sin θ cos( −θ ) = cosθ tan( −θ ) = − tan θ

14.  Work with one side at a time.
 We want both sides to be exactly the same.
 Start with either side
 Use algebraic manipulations and/or the basic
trigonometric identities until you have the same
expression as on the other side.

15. cot x sin x = cos x
LHS = cot x sin x
and RHS = cos x
cos x
= ⋅ sin x
sin x
= cos x
Since both sides are the same, the identity is verified.

16.  Start with the more complicated side
 Try substituting basic identities (changing all functions to be
in terms of sine and cosine may make things easier)
 Try algebra: factor, multiply, add, simplify, split up fractions
 If you’re really stuck make sure to:
Change everything on both sides to
sine and cosine.