1. WELCOME TO THE HIGHER MATHEMATICS CLASS
SHIPAN CHANDRA DEBNATH ASSISTANT PROFESSOR & HEAD OF THE DEPARTMENT DEPARTMENT OF MATHEMATICS CHITTAGONG CANTONMENT PUBLIC COLLEGE

2. THE QUADRANT SYSTEM Chapter - 7 Exercise -7(B) PAGE-
Book: Higher Mathematics
AKKHOR POTRA PROKASHONI

3. Learning Outcomes After complete this chapter students can
Determine the Trigonometric Ratios of Compound Angles

4. Definition of Compound angles : The sum or subtraction of two or more Angles is called Compound Angles. e.g. A+B, A-B, A+B+C etc.

5. II I III IV Quadrants (-,+) (+,+) (-,-) (+,-) X X’ O Y Y’
The cartesian plane is divided into four quadrants. Quadrants are numbered in anticlockwise direction. All abcissae in a given quadrant will have the same sign and all ordinates in a given quadrant will have the same sign.
(-,-)
(+,-)

6. Graph r O M
P(x,y) y x

7. Graph r O M
P(x,y) y x

8. 1.sin(A+B)=sinAcosB+cosAsinB
3.cos(A+B)=cosAcosB-sinAsinB
4.cos(A-B)=cosAcosB+sinAsinB
5.sin(A+B)+sin(A-B)=2sinAcosB
6.sin(A+B)-sin(A-B)=2sinBcosA
7.cos(A+B)+cos(A-B)=2cosAcosB
8.cos(A-B)-cos(A+B)=2sinAsinB

9. 9.sinC+sinD=2sin(C+D)/2cos(C-D)/2
10.sinC-sinD=2cos(C+D)/2sin(C-D)/2
11.cosC+cosD=2cos(C+D)/2cos(C-D)/2
12.cosC-cosD=-2sin(C+D)/2sin(C-D)/2
13.sin(A+B)sin(A-B)=sin2A-sin2B
14.sin(A+B)sin(A-B)=cos2B-cos2A
15.cos(A+B)cos(A-B)=cos2A-sin2B
16.cos(A-B)cos(A+B)=cos2B-sin2A

10. sin(A+B)=sinAcosB+cosAsinB
17. sin(2A)=2sinAcosA
cos(A+B)=cosAcosB-sinAsinB
18.cos(2A)=cos2A-sin2A
19.cos(2A)=2cos2A-1
20.cos(2A)=1-2sin2A
21.1+cos(2A)=2cos2A
22.1-cos(2A)=2sin2A

11. Apprise
What is slope?
What is Trigonometric ratio?
Find value of sin(1500 ),tan(-15750), cos(13050)

12. HOME TASK
Find the value of 1.sin12400
2. cot9400
3.cos4200 sin(-3000 )-sin(8700)cos(5700)
4. tan180+cos1920+tan1620+sin4380
Find the value of(i) sin{nπ+(-1)nπ/6} , n€z
(ii) cos{(2n+1)π+π/3}

13. THANKS TO ALL
HIPPARCHUS, FATHER OF TRIGONOMETRY