Trigonometry Summary

ACT Math · Axiom Academy

SUMMARY Trigonometry Unit Summary SOH-CAH-TOA, the unit circle, identities, graphing trig functions, and the Laws of Sines and Cosines — your complete review guide for ACT trig. Trig is only about 5–10% of the ACT Math section (3–6 questions) , but those questions cluster in the harder second half — mastering trig picks up points many students leave on the table. SOH-CAH-TOA is the foundation: , , — always labeled relative to the angle in question. The unit circle gives exact values for the key angles ( ), and "All Students Take Calculus" fixes the sign of each function by quadrant. The Pythagorean identity is the identity the ACT tests most; amplitude, period, and shifts come straight off . For non-right triangles, pick the law by what you're given: the Law of Sines for an angle–side pair, the Law of Cosines for SAS or SSS. Concept 1 SOH-CAH-TOA (Right Triangle Trig) The foundation of all ACT trig. You're given a right triangle with some sides or angles and asked to find a missing side, a missing angle, or a trig ratio. When to use: any right triangle — label the sides relative to the angle in question (opposite, adjacent, hypotenuse) first. Watch out for: "opposite" and "adjacent" depend on which angle you mean, not on the triangle's orientation. A circle of radius 1 centered at the origin. For any angle , the point on the circle is . Key angles: know sin and cos for and their radian forms.

This is the written version of the interactive lesson above. See the full ACT Math course.