Solving with Trigonometric Identities

Front

What is a trigonometric identity?

Back

A trigonometric identity is an equation involving trigonometric functions that is true for all values of the variable where both sides of the equation are defined.

Front

What is the Pythagorean identity?

Back

The Pythagorean identity states that sin²x + cos²x = 1 for any angle x.

Front

How do you factor the expression sin²x - sinx?

Back

sin²x - sinx = sinx(sinx - 1).

Front

What are the solutions to the equation sinθ = ½ on the interval [0, 2π)?

Back

θ = π/6 and θ = 5π/6.

Front

What is the general solution for the equation cos²θ - 1/2 = 0?

Back

The solutions are θ = π/4, 3π/4, 5π/4, and 7π/4.

Front

How do you solve the equation tan(x) + 1 = 2?

Back

Rearranging gives tan(x) = 1, leading to solutions x = π/4 and x = 5π/4.

Front

What is the factored form of sec²x - secx - 2?

Back

sec²x - secx - 2 = (secx - 2)(secx + 1).

Front

What is the sine function's range?

Back

The range of the sine function is [-1, 1].

Front

What is the cosine function's range?

Back

The range of the cosine function is [-1, 1].

Front

What is the tangent function's range?

Back

The range of the tangent function is all real numbers (-∞, ∞).