Solving Trigonometric Equations

Front

What is the solution to the equation tan θ = 0?

Back

The solutions are θ = 0, θ = π, θ = 2π. The value θ = π/2 is NOT a solution.

Front

What does the equation sin²x + cos²x = 2 imply?

Back

This equation has no solution because the maximum value of sin²x + cos²x is 1.

Front

Solve for 0≤x≤2π: 2sin²x - 5sinx + 2 = 0

Back

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

Front

What are the solutions for the equation 2sin²(x) - 3sin(x) + 1 = 0 over [0, 2π)?

Back

The solutions are x = π/6, x = 5π/6, and x = π/2.

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 Pythagorean identity in trigonometry?

Back

The Pythagorean identity states that sin²x + cos²x = 1.

Front

What is the period of the sine function?

Back

The period of the sine function is 2π.

Front

What is the period of the cosine function?

Back

The period of the cosine function is 2π.

Front

What is the value of sin(π/2)?

Back

sin(π/2) = 1.