Solving Trig Equations

Front

Define the range of the sine function.

Back

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

Front

What is the general solution for the equation sin(θ) = k, where k is a constant?

Back

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

Front

Solve the equation sin(θ) = 0 on the interval [0, 2π).

Back

θ = 0, π, 2π.

Front

What is the value of sin(θ) when θ = 3π/2?

Back

sin(3π/2) = -1.

Front

Solve the equation cos(θ) = 0 on the interval [0, 2π).

Back

θ = π/2, 3π/2.

Front

What is the period of the sine function?

Back

The period of the sine function is 2π.

Front

What is the value of cos(θ) when θ = π?

Back

cos(π) = -1.

Front

Solve the equation tan(θ) = 1 on the interval [0, 2π).

Back

θ = π/4, 5π/4.

Front

What is the relationship between sine and cosine?

Back

sin(θ) = cos(π/2 - θ).

Front

Define the unit circle in relation to trigonometric functions.

Back

The unit circle is a circle with a radius of 1 centered at the origin (0,0) in the coordinate plane, used to define sine and cosine values.