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The Humongous Book of Trigonometry Problems by W. Michael Kelley

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General and Exact Solutions

One vs. many answers

Note: Problems 9.15–9.17 describe three different ways to present the solution to the same trigonometric equation.

9.15    Identify the solutions to the equation sin θ = 0 on the interval 0 ≤ θ < 2π.

This is one loop around the coordinate plane. Notice that the interval includes 0 but excludes 2π. Both of those values represent the same angle—they both terminate on the positive x-axis—so there’s no need to include both.

According to the unit circle, sin θ = 0 when θ = 0 and θ = π.

Note: Problems 9.15–9.17 describe three different ways to present the solution to the same trigonometric equation.

9.16    List the values of θ for which the equation sin θ = 0 is true.

As Problem 9.15 states, sin ...

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