Solving Trig Equations (factoring)

Front

What is the definition of secant (sec) in trigonometry?

Back

Secant is the reciprocal of cosine: sec(x) = 1/cos(x).

Front

How do you factor the expression sec²x − secx − 2?

Back

(secx − 2)(secx + 1) is the factored form.

Front

What is the first step in solving the equation 2cos²x − 3cosx = 0?

Back

Factor out cosx: cosx(2cosx − 3) = 0.

Front

What are the solutions to the equation cosx(2cosx − 3) = 0?

Back

cosx = 0 or 2cosx − 3 = 0, leading to cosx = 3/2 (no solution) or cosx = 0.

Front

What is the double angle identity for sine?

Back

sin(2x) = 2sin(x)cos(x).

Front

How do you solve the equation 2sin x cos x = √2 cos x?

Back

Factor out cos x: cos x(2sin x - √2) = 0.

Front

What are the possible values of x when solving 2sin x cos x = √2 cos x on the domain [0, 2π)?

Back

x = π/2, 3π/2, π/4, 3π/4.

Front

What is the Pythagorean identity involving sine and cosine?

Back

sin²x + cos²x = 1.

Front

What is the relationship between secant and tangent?

Back

sec²x = 1 + tan²x.

Front

How do you convert the equation 2cos²x − 3cosx = 0 into a standard quadratic form?

Back

Rearrange to 2cos²x - 3cosx + 0 = 0.