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

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

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

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.

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. (-,-) (+,-)

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

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

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.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

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

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

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}

THANKS TO ALL HIPPARCHUS, FATHER OF TRIGONOMETRY