Skip to content

Physics Playground

Simulations How we teach Pricing

Language

Log in Start learning free

Loading…

Physics Playground

Built on open, peer-reviewed sources: OpenStax, The Feynman Lectures on Physics, HyperPhysics, NASA and NIST. See our sources.

Learn

Physics course
Math for Physics
Start with the math toolkit
Simulations
Glossary
Exercises
Past exams
Library
How we teach

Company

Pricing
Terms
Privacy
Contact

© 2026 Physics Playground. Made for the curious.Language

Exercises Trigonometry

Example 4 from Algebra and Trigonometry, 9.5 Solving Trigonometric Equations

Solving a Problem Involving a Single Trigonometric Function

Solve the problem exactly: $2 \sin^{2} θ - 1 = 0, 0 \leq θ < 2 π .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
As this problem is not easily factored, we will solve using the square root property. First, we use algebra to isolate $\sin θ .$ Then we will find the angles.
$\begin{matrix} 2 \sin^{2} θ - 1 & = & 0 \\ 2 \sin^{2} θ & = & 1 \\ \sin^{2} θ & = & \frac{1}{2} \\ \sqrt{\sin^{2} θ} & = & \pm \sqrt{\frac{1}{2}} \\ \sin θ & = & \pm \frac{1}{\sqrt{2}} = \pm \frac{\sqrt{2}}{2} \\ θ & = & \frac{π}{4}, \frac{3 π}{4}, \frac{5 π}{4}, \frac{7 π}{4} \end{matrix}$

How did it go?

PreviousSolve the Linear Trigonometric Equation Next Solving a Trigonometric Equation Involving Cosecant

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 9.5, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.