TRIGONOMETRIC RATIOS

2. SUBJECT : MATHEMATICS
CLASS : MATRIC/O-LEVEL
CHAPTER ( 3/4 ) : TRIGONOMETRY
LESSON NO : 04 OF 11
TOPIC : TRIGONOMETRIC
RATIOS OF 450

3. Q. What is trigonometry?
A. Trigonometry is that branch of mathematics which
deals with the solution of triangles.
Q. What are types of trigonometry?
A. There are two types of trigonometry
(i) Plane Trigonometry
(ii) Spherical Trigonometry
Q. What is triangle?
A. A closed figure which is formed by joining three
sides is called triangle.
Q. What is a right angled triangle?
A. A triangle having one angle of 900 is called right
angled triangle.

4. TRIGONOMETRIC RATIOS OF 450
 Procedure
 Derivation
 Related Examples

5. Easy way to remember trig
ratios:
SOH CAH TOA
Three Trigonometric Ratios
• Sine – abbreviated ‘sin’.
– Ratio: Sin θ = Perpendicular
Hypotenuse
• Cosine - abbreviated ‘cos’.
– Ratio: Cos θ = Base
Hypotenuse
• Tangent - abbreviated ‘tan’.
– Ratio: Tan θ = Perpendicular
Base
θ this is the symbol for
an unknown angle
measure. It’s name is
‘Theta’.

6. Specification of  ABC & SOH-CAH-TOA

7. Hyp
APer toSin(A) 
Hyp
AtoBaseCos(A) 
AtoBase
APer toTan(A) 
A
B
C
With Respect to angle A,
label the three sides

8. Three Trigonometric Ratios
=
=
=
Some People Have Curly Brown Hair Through Proper Brushing
Sin θ
Cos θ
Tan θ
Base
Perpendicular
Hypotenuse
Base
Perpendicular
Hypotenuse

9. TRIGONOMETRIC RATIOS OF 450
PerpHyp
A
B
C
a
b
c
) 450
450Triangle ABC is a right angled triangle
in which
 A =  B = 450
 C = 900
Procedure
Base 900

10. Procedure
a = b as A = B
By Pythagoras Theorem
c2 = a2 + b2
TRIGONOMETRIC RATIOS OF 450
PerpHyp
A
B
C
a
b
c
) 450
450
Since “a = b” so
c2 = a2 + a2
c2 = 2a2
Taking square root
2
2ac 
a2c 
Base

11. The lengths of sides of the triangle becomes
aABm 2
aBCm 
aACm 
TRIGONOMETRIC RATIOS OF 450
Procedure
a
a
PerpHyp
A
B
C) 450
450
a2c 
BACK
Base

12. Trigonometric Ratios OF 450
Derivation of Ratios
In ABC, we have
a
a
Perp
Hyp
A
B
C) 450
450
a2c 
2
1
a2
a
Sin450

2
1
a2
a
Cos450

1
a
a
Tan450

2Cosec450

2Sec450

10
Cot45
BACK
Base

13. TRIGONOMETRIC RATIOS OF 450

14. TRIGONOMETRIC RATIOS OF 450
Example
Prove that
Solution
L.H.S
2
3
cosec45
2
1
2sin45 00

00
cosec45
2
1
2sin45 
 2
2
1
2
1
2 
22
2x22x2 

2
3
22
6
22
24



BACK

15. TRIGONOMETRIC RATIOS OF 450
 Procedure
 Derivation
 Related Examples

17. Q. What is the value of sin 450 ?
A.
Q. What is the value of cos 450 ?
A.
Q. What is the value of tan 450 ?
A. 1
Q. What is the value of cosec 450 ?
A.
2
1
2
1
2
TRIGONOMETRIC RATIOS OF 450

18. TRIGONOMETRIC RATIOS OF
300 AND 600