The Trig Identity Match
Test your knowledge of trigonometric identities! Drag the expression card to the box containing its simplified equivalent.
Help & Instructions
▼- **New Card:** Click "New Card" to generate an identity to solve.
- **Match:** Drag the red card to the bin that holds its correct simplified form.
- **Rule Check:** The identities cover sum/difference angles and their related quadrant rules (e.g., $\sin(90^\circ-\theta)$).
- Master the trigonometric identities for sum, difference, and compound angles.
- Practice converting complex expressions into simplified forms.
- Reinforce quadrant rules and angle transformations.
This game is based on the **Trigonometric Sum and Difference Identities** (e.g., $\sin(A \pm B)$) and related **Complementary/Supplementary Angle Rules** (e.g., $\cos(180^\circ - \theta)$). These rules allow complex angles to be broken down into simpler expressions.
The Mathematics Behind the Puzzles
The rules derive from the unit circle and geometric proofs. For example, $\sin(A+B) = \sin A \cos B + \cos A \sin B$. The complementary angle identity $\cos(90^\circ - \theta) = \sin \theta$ is a special case of the sum identity where $A=90^\circ$ and $B=-\theta$ (or similar substitutions).
These identities are crucial in **physics** (wave analysis), **engineering** (signal processing), and advanced **calculus** for integration.
