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

TRIGONOMETRIC FUNCTIONS ?TRIGONOMETRIC FUNCTIONS ?

< 90 degrees< 90 degreesACUTE ANGLES ?ACUTE ANGLES ?

Functions of an angleFunctions of an angle

CIRCULAR FUNCTIONS ?CIRCULAR FUNCTIONS ? ≡ ≡ Trigno FunctionsTrigno Functions

TRIANGLESTRIANGLESRight AngledRight Angled ss

Involves :-Involves :-

Angles of Angles of Sides of Sides of

Relates :-Relates :-

SineSineCosine Cosine TangentTangent

Functions :-Functions :-

Ratios :-Ratios :-

Two Sides of Two Sides of Function(Function(acute angleacute angle) in that ) in that

(1) Opposite Side

(2) Adjacent Side

Angle aRight-Angled Trangle

(3) Hypotenuse

Angle a Right-Angled Trangle

Sine (sin)

Opposite SideHypotenuse

Opposite Side

Hypotenusesin ( a ) =

Angle aRight-Angled Trangle

Cosine (cos)

Adjacent Side

Hypotenuse

Adjacent Side

Hypotenusecos ( a ) =

Angle aRight-Angled Trangle

Tangent (tan)

Opposite Side

Adjacent Side

Opposite Side

Adjacent Sidetan ( a ) =

Adjacent Side

Hypotenusecos ( a ) =

I Cannot Remember !

Opposite Side

Hypotenusesin ( a ) =

Opposite Side

Adjacent Sidetan ( a ) =

SOH

CAH

TOA

B I G F O O T W O M A N

Inverse Trigo Functions

Opposite Side

Hypotenusesin ( a ) =

Opposite Side

Hypotenusea = 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 0.173648177

3 inverse Functions :

Sin-1 Cos-1 Tan-1

Try sin-1(0.174) Make sure CALC is Degree

Press [2ndF] then [sin]

Press number 0 . 1 7 4

Press [=]

ANS 10.02 º

2ndF

Same as ?

1

sin (0.174)

x

Adjacent Side = 10 cm

36º

y

Opposite Side

Adjacent Sidetan ( a ) =

x

10 cmtan ( 36 ) =

x = 10 tan ( 36 )

= 10 ( 0.727 )

= 7.27 cm

Try solving y usingSine or Cosine.

10cm

x

a

Hypotenuse = 20cm Opposite Side

Hypotenusesin ( a ) =

10

20sin ( a ) =

sin ( a ) = 0.5

a = sin-1 (0.5)

= 30º

Try solving x usingCosine or Tangent.

a 30º 45º 60º

sin(a) ½ 1/√2 (√3)/2

cos(a) (√3)/2 1/√2 ½

tan(a) 1/√3 1 √3

Equilateral Triange==> All angles 60°

Set side to 1 unit

Base halved by Centre Line

130º

60º

1

½ ½

x

Using Pythagoras' Theorem

√3 x =

2

45º

1

x

ySet one side to 1 unit

Isoceles x = 1

Using Pythagoras' Theorem

y = √2

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