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TRIGONOMETR
Y
 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
degrees
 Triangles on a sphere are also studied, in
spherical trigonometry.
 Trigonometry specifically deals with the
relationships between the sides and the angles of
triangles, that is, on the trigonometric functions,
and with calculations based on these functions.
Trigonometry
Right Triangle
 A triangle in which one angle
is equal to 90° is called right
triangle.
 The side opposite to the right
angle is known as hypotenuse.
AB is the hypotenuse
 The other two sides are
known as legs.
AC and BC are the legs
Trigonometry deals with Right Triangles
Pythagoras Theorem
In any right triangle, the area of the square whose
side is the hypotenuse is equal to the sum of areas of
the squares whose sides are the two legs.
In the figure
AB2
= BC2
+ AC2
Trigonometry
Trigonometry is the branch of mathematics that looks
at the relationship between the length of the sides
and the angles in a right angled triangle.
It helps us calculate the length of unknown sides,
without drawing the triangle, and it also helps us
calculate the size of an unknown angle without having
to measure it.
Let us look at a right angle triangle.
Trigonometry
O F
C
Hypotenuse
x0
Opposite
Adjacent
O F
C
Hypotenuse
y0
Opposite
Adjacent
The ‘Hypotenuse’ is always
opposite the right angle
The ‘Opposite’ is always
opposite the angle under
investigation.
The ‘Adjacent’ is always
alongside the angle under
investigation.
Adjacent , Opposite Side andAdjacent , Opposite Side and
Hypotenuse of a Right Angle TriangleHypotenuse of a Right Angle Triangle..
Adjacent side
Oppositeside
θθ
hypotenuse
φ
hypotenuse
Adjacentside
Opposite side
Definition of Sine Ratio.
θθ
For any right-angled triangle
Sinθ =
Opposite side
hypotenuses
Definition of Cosine Ratio.
θθ
For any right-angled triangle
Cosθ =
hypotenuses
Adjacent Side
Definition of Tangent Ratio.
θθ
For any right-angled triangle
tanθ =
Adjacent Side
Opposite Side
ConclusionConclusion
hypotenuse
sideopposite
sin =θ
hypotenuse
sidedjacenta
cos =θ
sidedjacenta
sideopposite
tan =θ
Make Sure
that the
triangle is
right-angled
14
Trigonometric ratios
Sine(sin) opposite side/hypotenuse
Cosine(cos) adjacent side/hypotenuse
Tangent(tan) opposite side/adjacent side
Cosecant(cosec) hypotenuse/opposite side
Secant(sec) hypotenuse/adjacent side
Cotangent(cot) adjacent side/opposite side
15
Values of trigonometric function
of Angle A
sinθ = a/c
cosθ = b/c
tanθ = a/b
cosecθ = c/a
secθ = c/b
cotθ = b/a
16
Values of Trigonometric function
0 30 45 60 90
Sine 0 0.5 1/√2 √3/2 1
Cosine 1 √3/2 1/√2 0.5 0
Tangent 0 1/ √3 1 √3 Not defined
Cosecant Not defined 2 √2 2/ √3 1
Secant 1 2/ √3 √2 2 Not defined
Cotangent Not defined √3 1 1/ √3 0
CONTEMPTORY
ANGLES
DONE BY – AARUSHI
,AMI,UNNATI &VIDHI

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Trigonometry

  • 2.  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 degrees  Triangles on a sphere are also studied, in spherical trigonometry.  Trigonometry specifically deals with the relationships between the sides and the angles of triangles, that is, on the trigonometric functions, and with calculations based on these functions. Trigonometry
  • 3. Right Triangle  A triangle in which one angle is equal to 90° is called right triangle.  The side opposite to the right angle is known as hypotenuse. AB is the hypotenuse  The other two sides are known as legs. AC and BC are the legs Trigonometry deals with Right Triangles
  • 4. Pythagoras Theorem In any right triangle, the area of the square whose side is the hypotenuse is equal to the sum of areas of the squares whose sides are the two legs. In the figure AB2 = BC2 + AC2
  • 5. Trigonometry Trigonometry is the branch of mathematics that looks at the relationship between the length of the sides and the angles in a right angled triangle. It helps us calculate the length of unknown sides, without drawing the triangle, and it also helps us calculate the size of an unknown angle without having to measure it. Let us look at a right angle triangle.
  • 6. Trigonometry O F C Hypotenuse x0 Opposite Adjacent O F C Hypotenuse y0 Opposite Adjacent The ‘Hypotenuse’ is always opposite the right angle The ‘Opposite’ is always opposite the angle under investigation. The ‘Adjacent’ is always alongside the angle under investigation.
  • 7. Adjacent , Opposite Side andAdjacent , Opposite Side and Hypotenuse of a Right Angle TriangleHypotenuse of a Right Angle Triangle..
  • 10. Definition of Sine Ratio. θθ For any right-angled triangle Sinθ = Opposite side hypotenuses
  • 11. Definition of Cosine Ratio. θθ For any right-angled triangle Cosθ = hypotenuses Adjacent Side
  • 12. Definition of Tangent Ratio. θθ For any right-angled triangle tanθ = Adjacent Side Opposite Side
  • 14. 14 Trigonometric ratios Sine(sin) opposite side/hypotenuse Cosine(cos) adjacent side/hypotenuse Tangent(tan) opposite side/adjacent side Cosecant(cosec) hypotenuse/opposite side Secant(sec) hypotenuse/adjacent side Cotangent(cot) adjacent side/opposite side
  • 15. 15 Values of trigonometric function of Angle A sinθ = a/c cosθ = b/c tanθ = a/b cosecθ = c/a secθ = c/b cotθ = b/a
  • 16. 16 Values of Trigonometric function 0 30 45 60 90 Sine 0 0.5 1/√2 √3/2 1 Cosine 1 √3/2 1/√2 0.5 0 Tangent 0 1/ √3 1 √3 Not defined Cosecant Not defined 2 √2 2/ √3 1 Secant 1 2/ √3 √2 2 Not defined Cotangent Not defined √3 1 1/ √3 0
  • 18. DONE BY – AARUSHI ,AMI,UNNATI &VIDHI