TRIGONOMETRIC IDENTITIES Co-function Identities Supplement

TRIGONOMETRIC IDENTITIES
Co-function Identities
sin θ = cos (π/2- θ )
sec θ = csc (π/2- θ )
tan θ = cot (π/2- θ )
Supplement Angle Identities
sin (π- θ ) = sin θ
cos (π- θ ) = - cos θ
tan (π- θ ) = - tan θ
csc (π- θ ) = csc θ
sec (π- θ ) = - sec θ
co t (π- θ ) = - cot θ
sin (π+ θ ) = - sin θ
cos (π+ θ ) = - cos θ
tan (π+ θ ) = tan θ
csc (π+ θ ) = - csc θ
sec (π+ θ ) = - sec θ
cot (π+ θ ) = cot θ
Negative Angle Identities
sin (- θ ) = - sin θ
cos (- θ ) = cos θ
tan (- θ ) = - tan θ
csc (- θ ) = - csc θ
sec (- θ ) = sec θ
cot (- θ ) = - cot θ
Addition and Subtraction Identities
Quotient Identities
sin θ
cos θ
1
sec θ =
cos θ
tan θ =
cos θ
1
=
sin θ
tanθ
1
=
sin θ
cot θ =
sin (A + B) =
sin A cos B + cos A sin B
cos (A + B) =
cos A cos B –sin A sin B
tan (A + B) =
tan A + tan B
1 –tan A tan B
Pythagorean Identities
sin (A –B) =
sin A cos B –cos A sin B
sin θ + cos θ = 1
cos (A –B) =
cos A cos B + sin A sin B
tan θ + 1 = sec θ
tan A –tan B
1 + tan A tan B
tan (A –B) =
Double-Angle Identities
sin 2 θ
= 2sin θ cos θ
cos 2 θ
= cos θ –sin θ
2
2
2
= 2cos θ –1
2
cscθ
2
2
2
2
cot θ + 1 = csc2 θ
Half-Angle Identities
sin
θ
2
=
±
1 –cos θ
2
cos
θ
2
=
±
1 + cosθ
2
tan
θ
2
=
±
1 –cos θ
1 + cosθ
= 1 –2sin2 θ
tan 2 θ
=
2tanθ
2
1 –tan θ
Product Identities
1
2
1
cosAsinB =
2
1
cosAcosB =
2
1
sinAsinB =
2
sinAcosB
=
( sin (A + B) + sin (A –B) )
( sin (A + B) –sin (A –B) )
( cos (A + B) + cos (A –B) )
( cos (A –B) –cos (A + B) )
Sum Identities
sinA + sinB
sinA –sinB
cosA + cosB
cosA –cosB
( A 2+ B
A+B
= 2cos(
2
A+B
= 2cos(
2
A+B
= - 2sin(
2
=
2sin
)cos( A 2–B
)sin( A 2–B
)cos( A 2–B
)sin( A 2–B
)
)
)
)