Trigonometric Identities Flashcards
What is the relationship between sin(x) and csc(x)?
sin(x) ⇒ 1/csc(x)
What is the relationship between cos(x) and sec(x)?
cos(x) ⇒ 1/sec(x)
What is the relationship between tan(x) and cot(x)?
tan(x) ⇒ 1/cot(x)
What is the relationship between csc(x) and sin(x)?
csc(x) ⇒ 1/sin(x)
What is the relationship between sec(x) and cos(x)?
sec(x) ⇒ 1/cos(x)
What is the relationship between cot(x) and tan(x)?
cot(x) ⇒ 1/tan(x)
What is the Pythagorean identity involving sin²(x) and cos²(x)?
sin²(x) + cos²(x) ⇒ 1
What is the identity involving tan²(x) and sec²(x)?
1 + tan²(x) ⇒ sec²(x)
What is the identity involving cot²(x) and csc²(x)?
1 + cot²(x) ⇒ csc²(x)
What is the double angle formula for sin(2x)?
sin(2x) ⇒ 2·sin(x)·cos(x)
What are the different forms of the double angle formula for cos(2x)?
cos(2x) ⇒ cos²(x) – sin²(x)
cos(2x) ⇒ 2·cos²(x) – 1
cos(2x) ⇒ 1 – 2·sin²(x)
What is the double angle formula for tan(2x)?
tan(2x) ⇒ 2·tan(x) / [1 – tan²(x)]
What is the formula for sin²(x) in terms of cos(2x)?
sin²(x) ⇒ [1 – cos(2x)] / 2
What is the formula for cos²(x) in terms of cos(2x)?
cos²(x) ⇒ [1 + cos(2x)] / 2
What is the formula for tan²(x) in terms of cos(2x)?
tan²(x) ⇒ [1 – cos(2x)] / [1 + cos(2x)]
What is the domain and range of arcsin(x)?
Domain: x ∈ [–1, 1]; Range: y ∈ [–π/2, π/2]
What is the domain and range of arccos(x)?
Domain: x ∈ [–1, 1]; Range: y ∈ [0, π]
What is the domain and range of arctan(x)?
Domain: x ∈ (–∞, ∞); Range: y ∈ (–π/2, π/2)
