Master SAT Geometry & Trig.
Circles, angles & solids.
Geometry & Trigonometry questions are high-yield points that reward spatial precision. Master standard circle equations, radian sector areas, special right triangles (30-60-90 & 45-45-90), and SOH-CAH-TOA trig identities.
Core Geometry & Trig Subtopics
Click any topic to explore theorem proofs, right-triangle ratios, and 3D formula sheets.
Circle Equations & Completing the Square
Finding circle centers $(h, k)$ and radius $r$ from standard form or general quadratic form $x^2 + y^2 + Dx + Ey + F = 0$.
(x - h)² + (y - k)² = r²Arc Length & Sector Area
Using radian measure ($\theta$) and degree proportions ($\theta/360$) for circle perimeters, arc lengths, and shaded sector slices.
s = rθ · Area = ½r²θRight-Triangle Trigonometry
Definitions of $\sin, \cos, \tan$, complementary angle relationship $\sin(x) = \cos(90^\circ - x)$, and unit circle coordinates.
sin(θ) = Opp/Hyp · cos(90-θ) = sin(θ)Special Right Triangles (30-60-90 & 45-45-90)
Ratio rules ($x : x\sqrt{3} : 2x$ and $x : x : x\sqrt{2}$) for rapid exact-value calculations without square root calculators.
30-60-90: 1 : √3 : 2Similarity & Angle-Angle Proofs
Proportional side lengths, scale factor $k$, perimeter scale $k$, and area scaling $k^2$ in overlapping similar triangles.
Area Ratio = (Side Ratio)²3D Volume & Surface Area
Right circular cylinders, cones, pyramids, rectangular solids, and spheres utilizing official SAT test-day reference sheet formulas.
V_cylinder = πr²h · V_cone = ⅓πr²hType Unfactored Circle Equations Directly
Never spend 2 minutes completing the square manually on test day. Type `x² + y² - 6x + 8y = 24` directly into Desmos. Tap the perimeter edges to find the center $(3, -4)$ and calculate radius $r = 7$ in 5 seconds.
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