OGM.13.TRG
Open Global Math Standards 2026™ · 12th Grade
Advanced Trigonometry, Analytic Identities, and Periodic Modeling
Grade12th Grade
SubjectMath
Levelstrand
Child standards (4)
- OGM.13.TRG.1Define trigonometric ratios and functions on the unit circle in radians and degrees, determine exact values at special angles, calculate reference angles, arc length, sector area, and solve problems involving angular and linear velocity.
- OGM.13.TRG.2Define, graph, and evaluate reciprocal trigonometric functions (secant, cosecant, cotangent) and inverse trigonometric functions (arcsin, arccos, arctan), specifying their principal domains and ranges.
- OGM.13.TRG.3Construct proofs of trigonometric identities including Pythagorean ($\\sin^2 \\theta + \\cos^2 \\theta = 1, 1 + \\tan^2 \\theta = \\sec^2 \\theta, 1 + \\cot^2 \\theta = \\csc^2 \\theta$), compound angle, double angle, and harmonic form conversions $R\\cos(\\theta \\pm \\alpha)$ and $R\\sin(\\theta \\pm \\alpha)$; solve trigonometric equations in specified intervals.
- OGM.13.TRG.4Apply trigonometry, small angle approximations ($\sin\theta \approx \theta$, $\cos\theta \approx 1 - \frac{\theta^2}{2}$, $\tan\theta \approx \theta$), the Law of Sines, the Law of Cosines, and area formulas to solve geometric, bearing, navigational, and periodic physical phenomena.