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 7 from Algebra and Trigonometry, 9.3 Double-Angle, Half-Angle, and Reduction Formulas

Using a Half-Angle Formula to Find the Exact Value of a Sine Function

Find $\sin (15°)$ using a half-angle formula.

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
Since $15° = \frac{30°}{2},$ we use the half-angle formula for sine:
$\begin{matrix} \sin \frac{30°}{2} & = & \sqrt{\frac{1 - \cos 30°}{2}} \\ = & \sqrt{\frac{1 - \frac{\sqrt{3}}{2}}{2}} \\ = & \sqrt{\frac{\frac{2 - \sqrt{3}}{2}}{2}} \\ = & \sqrt{\frac{2 - \sqrt{3}}{4}} \\ = & \frac{\sqrt{2 - \sqrt{3}}}{2} \end{matrix}$
Remember that we can check the answer with a graphing calculator.

How did it go?

PreviousUsing the Power-Reducing Formulas to Prove an Identity Next Finding Exact Values Using Half-Angle Identities

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 9.3, 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.