Trigonometry
Sine, cosine, tangent and their applications — about 7% of the ACT Math test.
8 skill topics sit under Trigonometry on the ACT Math taxonomy. Each one has its own dedicated page with concept notes and six worked practice questions. Work through the list top to bottom, or jump straight to the topic you struggle with.
This category accounts for a meaningful slice of your overall math score, so spend the time. The fastest way to gain points is to convert one weak topic per week into a strong one — not to skim every topic at surface depth.
Need the formulas at a glance? See the Trigonometry formula sheet. Studying for a specific score range? Use the score-band guides to focus on the topics that move the needle for your current score.
All Trigonometry topics
Sine, Cosine and Tangent
Use the right-triangle definitions of the three primary trig ratios.
Open topic
SOH-CAH-TOA Applications
Apply trig ratios to solve problems involving angles of elevation and depression.
Open topic
Basic Trig Identities
Use sin²θ + cos²θ = 1 and tan θ = sin θ / cos θ to simplify expressions.
Open topic
Law of Sines
Use a/sin A = b/sin B = c/sin C in non-right triangles.
Open topic
Law of Cosines
Use c² = a² + b² − 2ab·cos C to find a side or angle of a non-right triangle.
Open topic
Graphs of Trig Functions
Read amplitude, period, phase shift and vertical shift from y = a·sin(b(x − c)) + d.
Open topic
Inverse Trig Functions
Use sin⁻¹, cos⁻¹ and tan⁻¹ to find an angle from a ratio.
Open topic
Solving Trig Equations
Solve sin x = k, cos x = k and tan x = k on a given interval.
Open topic
Recommended study order
If this category is brand new to you, start with the first three topics in the list above — they tend to be the most foundational. Then work outward to the others. If you're already comfortable, go straight to a recent past paper, identify which Trigonometry question you missed, and drill that specific topic page.
For broader test-prep advice, see our study tips. For real test reference, browse the ACT Math past paper index.