Solving Trig Equations

Front

What is the range of the sine function?

Back

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

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 sinθ = k?

Back

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

Front

What is the general solution for cosθ = k?

Back

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

Front

What are the angles where sinθ = 1?

Back

The angle where sinθ = 1 is θ = π/2 + 2nπ, where n is any integer.

Front

What are the angles where sinθ = -1?

Back

The angle where sinθ = -1 is θ = 3π/2 + 2nπ, where n is any integer.

Front

What are the angles where cosθ = 1?

Back

The angle where cosθ = 1 is θ = 2nπ, where n is any integer.

Front

What are the angles where cosθ = -1?

Back

The angle where cosθ = -1 is θ = π + 2nπ, where n is any integer.

Front

How do you solve the equation 2sinθ + 3 = 2?

Back

First, isolate sinθ: 2sinθ = -1, then sinθ = -1/2. The solutions are θ = 7π/6, 11π/6.

Front

What is the solution for sinθ = 1/2 on the interval [0, 2π)?

Back

The solutions are θ = π/6 and θ = 5π/6.