Unit 4 Summary

Calculus Readiness · Axiom Academy

SUMMARY Unit 4 Summary: Trigonometry Essentials The unit circle, identities, graphs, and equations you just mastered — the load-bearing trig that every calculus derivative and integral runs through. The unit circle is the foundation. A point at angle has coordinates — that one sentence explains , the parities, and every special-angle value. Special angles should be instant. Reconstruct from the 30-60-90 and 45-45-90 triangles, then let ASTC carry the signs into every quadrant. Identities are algebraic tools, not decorations. Pythagorean, sum/difference, and double-angle formulas rewrite expressions — in calculus that rewrite is the difference between "I can integrate this" and "I'm stuck." Sine and cosine graphs have structure. Read in order: amplitude |A| , period , phase shift C/B , vertical shift D . Trig equations have infinitely many solutions. Find the base solution in one period, then add (or for tangent) to capture them all. Inverse trig gives one specific answer. Restricted ranges keep , , true functions — always watch the range. A point on the unit circle at angle has coordinates . That single fact unlocks everything else: why , why sine is odd and cosine is even, and where every special-angle value comes from. When to use: any time you need an exact value or the sign of a trig function. Watch out for: mixing up which coordinate is sine — y is sine, x is cosine.

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