20 flashcards · Shared on 19 August 2026 by AtomAI Library
Flip each card to check yourself.
Which equation is the fundamental Pythagorean identity?
sin²x + cos²x = 1
Which equation is the fundamental Pythagorean identity?
sin²x + cos²x = 1
How is tan x expressed in terms of sine and cosine, where cos x ≠ 0?
sin x / cos x
Which reciprocal identity defines sec x?
sec x = 1 / cos x
Complete the identity 1 + tan²x = …
sec²x
Which is the correct angle-addition formula for sin(a + b)?
sin a cos b + cos a sin b
What is the expansion of cos(a − b)?
cos a cos b + sin a sin b
Which double-angle identity is correct?
sin 2x = 2 sin x cos x
Which expression is equal to cos 2x?
cos²x − sin²x
How does sine behave when its angle is negated?
sin(−x) = −sin x
What is the smallest positive period of tan x?
π
For integer n, what is the general solution of sin x = 0?
x = nπ
For integer n, which formula gives every solution of cos x = 0?
x = π/2 + nπ
If tan x = tan α, what is the general solution for integer n?
x = α + nπ
Which pair of families gives the general solution of sin x = sin α, where n is an integer?
x = α + 2nπ or x = π − α + 2nπ
Which formula represents all solutions of cos x = cos α, where n is an integer?
x = 2nπ ± α
What are the solutions of sin x = 1/2 on 0 ≤ x < 2π?
π/6 and 5π/6
Solve 2cos²x − 1 = 0 on 0 ≤ x < 2π.
x = π/4, 3π/4, 5π/4, 7π/4
For sin x ≠ 0, what does (1 − cos²x) / sin x simplify to?
sin x
Which transformation of sin x cos x = sin x preserves all solutions and allows use of the zero-product rule?
Rewrite it as sin x(cos x − 1) = 0
What must be considered after solving a trigonometric equation by squaring both sides?
Squaring can introduce extraneous solutions, so answers must be checked