Simplifying Trig Expressions

Front

What is the definition of secant (sec)?

Back

Secant is the reciprocal of cosine, defined as sec(x) = 1/cos(x).

Front

What is the Pythagorean identity involving secant?

Back

The Pythagorean identity is sec²(x) = 1 + tan²(x).

Front

How do you simplify tan²(x) using the Pythagorean identity?

Back

Using the identity, tan²(x) = sec²(x) - 1.

Front

What is the definition of cotangent (cot)?

Back

Cotangent is the reciprocal of tangent, defined as cot(x) = 1/tan(x).

Front

What is the relationship between cotangent and tangent?

Back

cot(x) = 1/tan(x) and tan(x) = 1/cot(x).

Front

What is the definition of tangent (tan)?

Back

Tangent is defined as tan(x) = sin(x)/cos(x).

Front

What is the value of tan(90°)?

Back

tan(90°) is undefined because cos(90°) = 0.

Front

How do you simplify the expression sin²(x) + cos²(x)?

Back

sin²(x) + cos²(x) = 1, which is a fundamental trigonometric identity.

Front

What is the definition of sine (sin)?

Back

Sine is defined as sin(x) = opposite/hypotenuse in a right triangle.

Front

What is the definition of cosine (cos)?

Back

Cosine is defined as cos(x) = adjacent/hypotenuse in a right triangle.