Proving Trig Identities

Front

What is the definition of csc(x)?

Back

csc(x) is the cosecant function, defined as 1/sin(x).

Front

What is the definition of sec(x)?

Back

sec(x) is the secant function, defined as 1/cos(x).

Front

What is the definition of cot(x)?

Back

cot(x) is the cotangent function, defined as 1/tan(x) or cos(x)/sin(x).

Front

What is the Pythagorean identity involving sin and cos?

Back

sin²(θ) + cos²(θ) = 1.

Front

What is the relationship between tan(x) and sec(x)?

Back

tan²(x) + 1 = sec²(x).

Front

What is the relationship between cot(x) and csc(x)?

Back

cot²(x) + 1 = csc²(x).

Front

How do you simplify tan²(x) - sec²(x)?

Back

tan²(x) - sec²(x) = -1.

Front

What is the first step in verifying a trigonometric identity?

Back

Pick a side to simplify.

Front

What is the equivalent of sin(x) in terms of csc(x)?

Back

sin(x) = 1/csc(x).

Front

What is the equivalent of cos(x) in terms of sec(x)?

Back

cos(x) = 1/sec(x).