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Concept · Geometry & Algebra
Trigonometry
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A Geometry & Algebra set, untimed
Named traps
8 ways this goes wrong.
Each is a named misconception the questions are built to catch. Open one for the move that tempts, and the fix.
- Case-analysis value missedMisses one valid value of sin·cos (or similar) by dropping a sign/case in identity reduction.→
- Degree-radian factor invertedMultiplies by 180/π instead of π/180 (or mishandles the minutes part).→
- Law of cosines arrangement wrongPlugs sides into the wrong cosine-rule arrangement when finding an angle.→
- Quadrant sign errorAssigns the wrong sign to a trig value based on quadrant.→
- Reduction/co-function shift wrongUses the wrong reduction/phase-shift identity (e.g. sin(x+π/2)).→
- Stretch vs compression confusedUses 2x vs x/2 incorrectly for a horizontal stretch/compression, or changes amplitude instead of period.→
- Terminal-side radius wrongComputes r=√x2+y2 incorrectly or swaps sine and cosine ratios for a terminal-side point.→
- tan(A+B) formula misappliedMis-signs/mis-structures tan(A+B), or forgets A+B+C=π so C=π-(A+B).→
Key formulas
11- Degree-radianradians = degrees × π/180
- Pythagorean identitysin2 x + cos2 x = 1tan x = sin x / cos x
- Periods2π for sin and cos, π for tan
- Sum/differencesin(A±B)=sinA cosB ± cosA sinBcos(A±B)=cosA cosB ∓ sinA sinBtan(A±B)=(tanA ± tanB)/(1 ∓ tanA tanB)
- Double-anglesin 2x = 2 sin x cos xcos 2x = cos2 x − sin2 x = 2cos2 x − 1 = 1 − 2sin2 x
- Half-angle and product-to-sum / sum-to-product formulas (standard set)
- Triangle angle sumA + B + C = π (so C = π − (A+B))
- Sine Rulea/sin A = b/sin B = c/sin C = 2R
- Law of Cosinesc2 = a2 + b2 − 2ab cos C
- Triangle areaS = (1/2)ab sin C
- y = A sin(ωx + φ): amplitude A, period 2π/ωhorizontal stretch by factor k uses ω → ω/k
Shaky underneath?
If the concept underneath still feels loose, patch it here before coming back to CSCA questions.
FoundationsPrecalculus bridgeAlgebra 2 foundations