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Trigonometric Identities
6 Reciprocal Identities:
sin 𝜃 =
tan 𝜃 =
csc θ =
Exercise:
1
csc 𝜃
1
cot 𝜃
1
sin 𝜃
1
cos θ =
cot θ =
sec 𝜃
1
tan 𝜃
sec θ =
1
cos 𝜃
𝑜
𝑎
ℎ
ℎ
𝑜
3
𝑎
4
5
5
3
4
If sin 𝜃 = , then csc 𝜃 = _____ If cos 𝜃 = , then sec 𝜃 = _____
If tan 𝜃 = , then cot 𝜃 = _____ If cot 𝜃 = , then tan 𝜃 = _____
If csc 𝜃 = , then sin 𝜃 = _____ If sec 𝜃 = , then cos 𝜃 = _____
2 Quotient Identities:
Tan 𝜃 =
sin 𝜃
𝑐𝑜𝑠𝜃
Cot 𝜃 =
cos 𝜃
sin 𝜃
3 Pythagorean Identities:
1)
Original:
sin2𝜃 + cos 2𝜃 = 1
2)
tan2 θ + 1 = sec2 θ
3)
1 + cot2 θ = csc2 θ
Rewritten: