Solving Trig Equations

Front

Define the sine function in terms of a right triangle.

Back

In a right triangle, the sine of an angle θ is the ratio of the length of the opposite side to the length of the hypotenuse.

Front

What is the range of the sine function?

Back

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

Front

What is the general solution for sin(θ) = k?

Back

The general solution is θ = arcsin(k) + 2nπ or θ = π - arcsin(k) + 2nπ, where n is any integer.

Front

Solve for θ: sin(θ) = 0.

Back

θ = nπ, where n is any integer.

Front

What is the cosine function in terms of a right triangle?

Back

In a right triangle, the cosine of an angle θ is the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

What is the range of the cosine function?

Back

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

Front

What is the general solution for cos(θ) = k?

Back

The general solution is θ = ±arccos(k) + 2nπ, where n is any integer.

Front

Solve for θ: cos(θ) = 0.

Back

θ = (2n + 1)π/2, where n is any integer.

Front

What is the tangent function in terms of sine and cosine?

Back

The tangent function is defined as tan(θ) = sin(θ)/cos(θ).

Front

What is the range of the tangent function?

Back

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