Trigonometric Functions by Priyanshi Negi

Angle

Degree Measure

Radian Measure

Relation

180°=π radian

Trigonmetric Identities

Signs of Trigonometric Functions

I Quadrant (All +ve)

Graphs of Trigonometric Functions

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FOR

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Trigonmetric Equations

PRINCIPAL SOLUTIONS

GENERAL SOLUTIONS deleted

0 ≤ x < 2π

sinx

tanx

cosx

sum of angles (A + B)

difference of angles(A-B)

angles like 2A

angles like 3A

cos 2A = (cos²A-sin²A)= 2cos²A-1 = 1-2sin²A = (1-tan²A)/1+tan²A)

sin(A+B)=sinAcosB+cosAsinB

cos(A+B)=cosAcosB-sinAsinB

tan(A+B)=(tanA+tanB)/(1-tanAtanB)

cot(A+B)=(cotBcotA-1)/(cotB+cotA)

cos(A-B)=cosAcosB+sinAsinB

tan(A-B)=(tanA-tanB)/(1+tanAtanB)

cot(A-B)=(cotAcotB+1)/(cotB-cotA)

sin(A-B)=sinAcosB-cosAsinB

sin2A = 2sinAcosA = 2tanA/(1+tan²A)

tan2A = 2tanA/(1-tan²A)

sin3A=3sinA-4sin³A

cos3A=4cos³A-3cosA

tan3A=(3tanA-tan³A)/(1-3tan²A)

1°=60',1'=60''

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}

II Quadrant(only sin and cosec are +ve)

III Quadrant(only tan and cot are +ve)

IV Quadrant(only cos and sec are +ve)

eg: sinx =0

x=0,π

eg: sinx =0

x=nπ,n is an integer

r=radius, l=length of arc, a=angle subtended at centre(in radian)

l=ra