Basics-Trignometry-Lecture Slides, Slides of Trigonometry

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Trigonometry

Pythagoras Theorem &

Trigo Ratios of Acute

Angles

Pythagoras Theorem

a

2

+ b

2

= c

2

where c is the hypotenuse while a

and b are the lengths of the other two

sides.

c

b

a

Trigo Ratios of Acute angles

Hypotenuse = AB

Adjacent = AC

Opposite= BC



A

B

C

X

Y

Z

Hypotenuse = XZ

Adjacent = XY

Opposite= YZ

Trigo Ratios of Acute angles



O

P

Q

hypotenuse

adjacent

opposite

Tangent ratio Cosine ratio^ Sine ratio

tan cos sin

Trigo Ratios of Acute angles

OQ

PQ   adjacent

opposite

tan 

OP

OQ

hypotenuse

adjacent

cos 

O

P

Q

hypotenuse

adjacent

opposite

OP

PQ

hypotenuse

opposite

sin 



TOA CAH SOH

Exercise 1



12

5

adjacent

opposite

tan   

13

12

hypotenuse

adjacent

cos   

13

5

hypotenuse

opposite

sin   



3

4

adjacent

opposite

tan   

5

3

hypotenuse

adjacent

cos   

5

4

hypotenuse

opposite sin   

Exercise 2

4

3 tan A 

5

4 cos A 

5

3 sin A 

A

8

15 tan B 

17

15 sin B 

17

8 cos B 

B

29

20 cos C 

29

21 sin C 

20

21 tan C 

C

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Exercise 3

tan 45  1



cos 60  0. 5



sin 60  0. 866



tan 23  0. 424



cos 30  0. 866



sin 0. 5  0. 00873



Exercise 5

sin  = 0.

 = sin

cos  = 0.

 = cos

tan  = 4.

 = tan

Exercise 5

sin  = 0.

 = sin

cos  = 0.

 = cos

tan  = 0.

 = tan

Further Examples 1

B

A C

7 cm

8 cm

8 cm

D

E

54.8°

In the diagram, BCE is a straight line,

angle ECD = 54.8° and angle CDE =

angle ACB = 90°.

BC = 7 cm and AC = CE = 8 cm.

Calculate

angle CED = 180° − 90° − 54.8° = 35.2°

angle CED?

Further Examples 1

B

A C

7 cm

8 cm

8 cm

D

E

54.8°

In the diagram, BCE is a straight line,

angle ECD = 54.8° and angle CDE =

angle ACB = 90°.

BC = 7 cm and AC = CE = 8 cm.

Calculate

angle DCB = 180° − 54.8° = 125.2°

angle DCB?

Further Examples 1

B

A C

7 cm

8 cm

8 cm

D

E

54.8°

the length of ED?

CD

ED   adjacent

opposite tan 54. 8



hypotenuse 8

adjacent cos 54. 8

CD  



hypotenuse 8

opposite sin 54. 8

ED  



ED cm

ED

8 sin 54. 8 6. 537 ... 6. 54

sin 54. 8





Further Examples 1

B

A C

7 cm

8 cm

8 cm

D

E

54.8°

the length of AE?

adjacent

opposite tan? 

hypotenuse

adjacent cos? 

hypotenuse

opposite sin? 

AE cm

AE

128 11. 3137 ... 11. 3

8 8

2 2 2

  

 