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Trigonometric Functions by Priyanshi Negi - Coggle Diagram
Trigonometric Functions by Priyanshi Negi
Angle
Degree Measure
Relation
180°=π radian
1°=60',1'=60''
Radian Measure
r=radius, l=length of arc, a=angle subtended at centre(in radian)
l=ra
Trigonmetric Identities
FOR
sum of angles (A + B)
sin(A+B)=sinAcosB+cosAsinB
cos(A+B)=cosAcosB-sinAsinB
tan(A+B)=(tanA+tanB)/(1-tanAtanB)
cot(A+B)=(cotBcotA-1)/(cotB+cotA)
difference of angles(A-B)
cos(A-B)=cosAcosB+sinAsinB
tan(A-B)=(tanA-tanB)/(1+tanAtanB)
cot(A-B)=(cotAcotB+1)/(cotB-cotA)
sin(A-B)=sinAcosB-cosAsinB
angles like 2A
cos 2A = (cos²A-sin²A)= 2cos²A-1 = 1-2sin²A = (1-tan²A)/1+tan²A)
sin2A = 2sinAcosA = 2tanA/(1+tan²A)
tan2A = 2tanA/(1-tan²A)
angles like 3A
sin3A=3sinA-4sin³A
cos3A=4cos³A-3cosA
tan3A=(3tanA-tan³A)/(1-3tan²A)
2cos x cos y = cos ( x + y) + cos ( x – y)
– 2sin x sin y = cos (x + y) – cos (x – y)
2sin x cos y = sin (x + y) + sin (x – y)
2 cos x sin y = sin (x + y) – sin (x – y)
cosA+cosB=2cos{(A+B)/2}cos{(A-B)/2}
cosA-cosB=-2sin{(A+B)/2}sin{(A-B)/2}
sinA+sinB=2sin{(A+B)/2}cos{(A-B)/2}
sinA-sinB=2cos{(A+B)/2}sin{(A-B)/2}
Signs of Trigonometric Functions
I Quadrant (All +ve)
II Quadrant(only sin and cosec are +ve)
III Quadrant(only tan and cot are +ve)
IV Quadrant(only cos and sec are +ve)
Graphs of Trigonometric Functions
cosx
tanx
sinx
Trigonmetric Equations
PRINCIPAL SOLUTIONS
0 ≤ x < 2π
eg: sinx =0
x=0,π
GENERAL SOLUTIONS
deleted
eg: sinx =0
x=nπ,n is an integer
