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BetterGrades Precalculus · Unit 11 · Unit map

Trigonometric Identities and Equations

Is (1-cos^2 x)/sin x=sin x an identity? State the exact common domain on which the equality is valid.

Precalculus · Unit 11

The lesson path

Is (1-cos^2 x)/sin x=sin x an identity? State the exact common domain on which the equality is valid.

Core sequence

Trigonometric Identities and Equations

Move in order when the material is new, or enter at the exact skill you need.

  1. 01Identities, equations, and proof strategyDistinguish identities from conditional equations and use valid one-sided transformation strategies.
  2. 02Reciprocal, quotient, and Pythagorean identitiesDerive and apply the fundamental trig identities from unit-circle coordinates.
  3. 03Verifying identities strategicallySelect factoring, common denominators, conjugates, or sine-cosine conversion to verify identities.
  4. 04Sum and difference formulasDerive and apply sine, cosine, and tangent sum and difference formulas.
  5. 05Double-angle formulasDerive and use double-angle identities, including three equivalent cosine forms.
  6. 06Half-angle and power-reduction formulasDerive half-angle and power-reduction identities and select signs using quadrant information.
  7. 07Product-to-sum and sum-to-product formulasConvert products and sums of trig functions to alternate forms and interpret signal combinations.
  8. 08Equations using fundamental identitiesSolve trig equations by converting functions, factoring, and applying fundamental identities.
  9. 09Quadratic-form trigonometric equationsUse substitution and algebraic solving for equations quadratic in a trig function.
  10. 10Multiple-angle equationsSolve equations involving sin(nx), cos(nx), or tan(nx) and translate solution families back to xx.
  11. 11General solutions and interval restrictionsWrite complete periodic solution families and extract all solutions from specified intervals.
  12. 12Exact and numerical trigonometric equation solvingUse graphing, bracketing, and numerical methods for trig equations without convenient exact solutions.
Source record

References used for this unit

  • Sundstrom & Schlicker, Trigonometry, Chapter 4
  • Lippman & Rasmussen, Precalculus Vol. 2, Chapter 7
  • Yoshiwara, Trigonometry, Chapters 5, 7, and 8
  • Corral, Trigonometry, Chapters 3 and 6

The learner copy is original BetterGrades material informed by these rights-separated references; no long source passage is reproduced.