Present by: Akira Makino ( L ) Jerry Zhang Nathan Teo Zhao Boning

TRIGONOMETRIC FUNCTIONS ? < 90 degrees < 90 degrees ACUTE ANGLES ? Functions of an angle CIRCULAR FUNCTIONS ? ≡ Trigno Functions ≡ Trigno Functions

TRIANGLES Right Angled  s Involves :- Angles of  Sides of  Relates :- Sine Cosine Tangent Functions :- Ratios :- Two Sides of  Function(acute angle) in that 

(1) Opposite Side (2) Adjacent Side Angle a Right-Angled Trangle (3) Hypotenuse

< 1 Angle a Right-Angled Trangle Sine (sin) Opposite Side Hypotenuse Opposite Side Hypotenuse sin ( a ) =

< 1 Angle a Right-Angled Trangle Cosine (cos) Adjacent Side Hypotenuse Adjacent Side Hypotenuse cos ( a ) =

Angle a Right-Angled Trangle Tangent (tan) Opposite Side Adjacent Side Opposite Side Adjacent Side tan ( a ) =

Adjacent Side Hypotenuse cos ( a ) = I Cannot Remember ! Opposite Side Hypotenuse sin ( a ) = Opposite Side Adjacent Side tan ( a ) = SOH CAH TOA B I G F O O T W O M A N

Inverse Trigo Functions Opposite Side Hypotenuse sin ( a ) = Opposite Side Hypotenuse a = sin -1 sin -1 ( x ) ≠ sin ( x ) 1 sin -1 same as arcsin sin -1 notation only

3 units in toggles: Degree Radians Gradient 360 Degree in a circle 2π Radian in a circle 400 Gradient in a circle

3 Functions : Sine Cosine Tangent Try sin (10º) Make sure CALC is Degree Press [sin] Press number 1,0 Press [=] ANS

3 inverse Functions : Sin -1 Cos -1 Tan -1 Try sin -1 (0.174) Make sure CALC is Degree Press [2 nd F] then [sin] Press number Press [=] ANS º 2 nd F Same as ? 1 sin (0.174)

x Adjacent Side = 10 cm 36 º y Opposite Side Adjacent Side tan ( a ) = x 10 cm tan ( 36 ) = x = 10 tan ( 36 ) = 10 ( ) = 7.27 cm Try solving y using Sine or Cosine.

10cm x a Hypotenuse = 20cm Opposite Side Hypotenuse sin ( a ) = sin ( a ) = sin ( a ) = 0.5 a = sin -1 (0.5) = 30 º Try solving x using Cosine or Tangent.

a 30º45º60º sin(a)½1/√2(√3)/2 cos(a)(√3)/21/√2½ tan(a)1/√31√3

Equilateral Triange ==> All angles 60° Set side to 1 unit Base halved by Centre Line 1 30 º 60 º 1 ½½ x Using Pythagoras' Theorem √3 x = 2

45 º 1 x y Set one side to 1 unit Isoceles x = 1 Using Pythagoras' Theorem y = √2

Present by: Akira Makino ( L ) Jerry Zhang Nathan Teo Zhao Boning