Trigonometric Identities
Trigonometric Identities
An “Identity” is a math statement that is ALWAYS true.
An “Identity” is a math statement that is ALWAYS true.
The left-hand side and the right-hand side of the equation can
be substituted for each other as needed.
The left-hand side and the right-hand side of the equation can
be substituted for each other as needed.
Partial List of Identities
Partial List of Identities
sin2 𝑥 + cos 2 𝑥 = 1
sin2 𝑥 + cos 2 𝑥 = 1
cos 2 𝑥 = 1 − sin2 𝑥
cos 2 𝑥 = 1 − sin2 𝑥
sin2 𝑥 = 1 − cos 2 𝑥
sin2 𝑥 = 1 − cos 2 𝑥
tan 𝑥 =
cot 𝑥 =
csc 𝑥 =
sec 𝑥 =
sin 𝑥
cos 𝑥
cos 𝑥
sin 𝑥
1
sin 𝑥
1
cos 𝑥
1 + cot 2 𝑥 = csc 2 𝑥
tan 𝑥 =
cot 𝑥 =
sin 𝑥 =
cos 𝑥 =
1
cot 𝑥
1
tan 𝑥
1
csc 𝑥
1
sec 𝑥
( divide 1st equation by sin2x )
tan 𝑥 =
cot 𝑥 =
csc 𝑥 =
sec 𝑥 =
sin 𝑥
cos 𝑥
cos 𝑥
sin 𝑥
1
sin 𝑥
1
cos 𝑥
1 + cot 2 𝑥 = csc 2 𝑥
1 = csc 2 𝑥 − cot 2 𝑥
1 = csc 2 𝑥 − cot 2 𝑥
cot 2 𝑥 = csc 2 𝑥 − 1
cot 2 𝑥 = csc 2 𝑥 − 1
tan2 𝑥 + 1 = sec 2 𝑥
( divide 1st equation by cos2x )
tan2 𝑥 + 1 = sec 2 𝑥
tan2 𝑥 = sec 2 𝑥 − 1
tan2 𝑥 = sec 2 𝑥 − 1
1 = sec 2 𝑥 − tan2 𝑥
1 = sec 2 𝑥 − tan2 𝑥
tan 𝑥 =
cot 𝑥 =
sin 𝑥 =
cos 𝑥 =
1
cot 𝑥
1
tan 𝑥
1
csc 𝑥
1
sec 𝑥
( divide 1st equation by sin2x )
( divide 1st equation by cos2x )