Basic Trig Identities — Quick Reference Cheatsheet

This is a one-page reference for Basic Trig Identities on the ACT math section. Use sin²θ + cos²θ = 1 and tan θ = sin θ / cos θ to simplify expressions. Use it as a printable cheatsheet before test day, or as a refresher right before you attempt the worked questions on the main Basic Trig Identities topic page.

What this topic is

A Basic Trig Identities question tests sine, cosine, tangent, identities, and the laws of sines and cosines. SOH-CAH-TOA must be automatic.

Core formulas you must memorise

• sin = opp/hyp ; cos = adj/hyp ; tan = opp/adj
• sin²θ + cos²θ = 1
• Law of sines: a/sin A = b/sin B = c/sin C
• Law of cosines: c² = a² + b² − 2ab cos C
• Common angles: 30° → ½, 45° → √2/2, 60° → √3/2

If any of these formulas are not yet automatic, drill them via the Trigonometry formula sheet. Memorisation is fastest when you write each formula out by hand five times in a row, then quiz yourself the next morning.

How to spot this question type on the test

ACT questions on Basic Trig Identities typically present in one of three ways: as a pure symbolic problem ("solve for x"), wrapped in a word problem (a real-world scenario you must translate), or hidden inside a longer multi-step question where Basic Trig Identities is just the first or last step. Train yourself to recognise the signature — a particular word, equation form, or diagram — and you will halve your reading time.

The 30-second decision

Check whether the calculator is in degrees or radians BEFORE punching in any numbers.

If you have 60 seconds before the question

Glance at the answer choices first. If they are widely spaced, estimate; if they are close, you must be exact. Sketch any diagram involved. Identify which of the formulas above applies. Then attempt — and if you cannot finish in 90 seconds, mark and move on. There is no penalty for guessing on either the SAT or the ACT, so always bubble in.

Drill set

Re-attempt the six worked Basic Trig Identities questions with this cheatsheet open. Then close it and re-attempt them from memory. If you can solve all six without peeking, this topic is locked in.

Related study material

For broader test-prep tactics, see our Basic Trig Identities strategy guide. For category-wide context, browse all Trigonometry topics. For score-targeted study plans, see the score-band guides.