ACT Math Geometry & Trigonometry: Complete Guide

Geometry and trigonometry together account for roughly 12–14 of the 45 ACT Math questions — a bigger share than on the SAT. Critically, the ACT does not provide a reference sheet with geometry formulas. You must have the area of a circle, triangle area, the Pythagorean theorem, and common Pythagorean triples (3-4-5, 5-12-13, 8-15-17) memorized.

Trigonometry is a significant ACT topic that barely appears on the SAT. The ACT tests SOHCAHTOA (right-triangle trig), the unit circle (values of sin/cos at 0°, 30°, 45°, 60°, 90°), basic trig identities (sin²θ + cos²θ = 1), and occasionally the law of sines or cosines. If you haven't studied trig, these 4–5 questions are low-hanging fruit after a focused review.

For triangle problems, check immediately whether you have a right triangle. If so, the Pythagorean theorem and SOHCAHTOA apply. If you see a 30-60-90 or 45-45-90 triangle, use the side ratios directly (1 : √3 : 2 and 1 : 1 : √2) — they're faster than computing from scratch.

For SOHCAHTOA questions, label all three sides of the right triangle (Opposite, Adjacent, Hypotenuse) relative to the angle in question before applying any ratio. Mislabeling is the #1 trig error.

For coordinate geometry, remember: slope = (y₂ − y₁)/(x₂ − x₁); midpoint = ((x₁+x₂)/2, (y₁+y₂)/2); distance = √((Δx)² + (Δy)²). The distance formula is the Pythagorean theorem in coordinate form — you don't need to memorize it separately.

Forgetting that the ACT gives no formula sheet. Students who rely on the SAT reference sheet are caught off guard. Memorize: circle area = πr², circumference = 2πr, sector area = (θ/360)πr², triangle area = ½bh.

Mislabeling opposite and adjacent in trig problems. "Opposite" is the side across from the angle, not the longest side. Label first, compute second.

On coordinate geometry circle problems, confusing the standard form (x − h)² + (y − k)² = r² — the center is (h, k) and the radius is √r², not r². Students often forget to take the square root.

Make a formula card for the ACT's missing reference sheet: triangle area, circle area, circumference, arc length, sector area, Pythagorean theorem, 30-60-90 and 45-45-90 ratios, SOHCAHTOA, and the unit circle values at 0°/30°/45°/60°/90°. Review it before every practice session for two weeks until recall is automatic.

Trigonometry is the highest-ROI ACT Math study area for most students who haven't seen it recently. Four focused hours on right-triangle trig and the unit circle can unlock 4–5 additional correct answers.