Trigonometry
Free lessons and practice worksheets for trigonometry.
Inverse Trigonometry
Inverse trigonometry transforms ratio values back into angle measures, making it essential for solving triangles and modeling periodic phenomena. When students see arcsin(1/2) = 30°, they're reversing the process they learned with regular sine functions.
3 min readTrigonometric Equations
Trigonometric equations challenge students to combine unit circle knowledge with algebraic problem-solving skills. These equations appear frequently on standardized tests and form the foundation for advanced calculus concepts.
3 min readTrigonometric Graphs
Teaching trigonometric graphs transforms from abstract formulas to visual understanding when students can identify amplitude, period, and phase shifts. The function y = 3 sin(2x - π/2) + 1 contains all the essential components students encounter from CCSS.HSF.TF.B.5 through UK A-Level Pure Mathematics.
3 min readTrigonometric Identities
Trigonometric identities transform complex expressions into manageable forms, turning a 15-minute algebra nightmare into a 3-step solution. These fundamental relationships between sine, cosine, tangent, and their reciprocals form the backbone of advanced mathematics, appearing in calculus, physics, and engineering applications daily.
3 min readTrigonometry (SOH CAH TOA)
The SOH CAH TOA mnemonic transforms intimidating trigonometry into manageable steps for finding sides and angles in right triangles. Students master this foundation in CCSS.HSG.SRT before tackling advanced applications like surveying and engineering. Understanding these 3 ratios unlocks problem-solving across construction, navigation, and physics.
3 min readUnit Circle
When students struggle with exact trigonometric values, they often default to decimal approximations like sin(30°) = 0.5 instead of the precise fraction 1/2. The unit circle provides a systematic framework for finding exact values at standard angles like 30°, 45°, 60°, and their multiples across all quadrants.
3 min read