2022 Spring | Trig

Course Coordinator:
- Nagy
- His webpage here
- Textbook here
Recitation Instructor:
- Winston Cheong
- winstonc@ksu.edu
- Zoom personal meeting room

Recitation Notes

Recit 5 (Feb 15, 2022) We covered material on HW 3: equation of a circle, bearing notation, linear equations "lines", vector arithmetic, unit circle.
- Addendum Feb 16, 2022: Added additional approach for #1 that students informed me of.
Recit 6 (Feb 22, 2022) We covered material on HW 4: evaluating trig functions over the entire unit circle, verifying trig identities, and disproving "false identities".
Recit 7 (Mar 01, 2022) We reviewed for Midterm 2: primarily went over the extra practice problems (verifying trig identities, transforming an angle to different quadrants).
- For additional practice with verifying trig identities:
  - Exercises at the end of Section 2.3 in Nagy's textbook.
  - OpenStax Precalc 2e > Section 7.1: Solving Trigonometric Equations with Identities (Try working through the examples and exercises).
Recit 8 (Mar 8, 2022) We covered material on HW 5: Reading off the equation of a sinusoidal function from its graph, the process for sketching a sinusoidal function.
- The formulas and step by step process are written out in my formula sheet / notes (see below)
- Related Desmos link
- Addendum to recit notes: Explicit calculations going from General Sinusoid to its standard form
- For additional practice with doing arithmetic with fractions:
  - Tyler Wallace's online textbook, Section 0.2.
  - Blackpenredpen's video "100 Fractions"
Recit 9 (March 22, 2022) We covered material on HW6: Evaluating trig(inverse_trig()) and inverse_trig(trig()), finding solutions to elementary trig equations.
Recit 10 (March 29, 2022) We covered material on HW7: Solving more complicated trig equations, dot product and skew product, vector geometry problems, turning angle and geometric angle.
- Additional practice with solving trig equations (with worked solutions): https://tutorial.math.lamar.edu/Problems/CalcI/TrigEquations.aspx
- Additional unit circle practice (with worked solutions): https://tutorial.math.lamar.edu/Problems/CalcI/TrigFcns.aspx
Recit 12 (April 12, 2022) We covered material on Hw8: Calculating area of paralleogram and triangle using vectors, calculating orthogonal projection, solving general triangles using law of sines and law of cosines.
- Obtuse triangle examples:
  - $a=15,\ b=7,\ c=9$
  - $a=20,\ b=5,\ \widehat{C} = 5^\circ$
Recit 13 (April 19, 2022) We covered material on Hw9: Area of triangle giving side/angle info, problems involving sum/difference formulas for sine/cosine/tangent.
Recit 14 (April 26, 2022) We covered material on Hw10: Problems involving double-angle, half-angle, product-to-sum, and sum-to-product formulas.
Recit 15 (May 3, 2022) We covered material on Hw11: Converting representations of complex numbers, using De Moivre's formula for powers and roots of complex numbers, finding all roots (real and complex) of a polynomial.

Videos

Trig resources

My unit circle cheatsheet here
My formula sheet / notes here
- This is a living document. Changes are still being made to it.
- Changelog:
  - Mar 1, 2022: Added margin notes for the supplement formulas, add $\pi$ formulas and "formulas for negatives". Added separator for post-midterm-2 material. Added section on sketching sinusoidal functions (Covered in Hw 5. Section 2.5 of Nagy's textbook).
  - Mar 29, 2022: Added Section 3.1 Material (dot product and skew product, dot/skew product theorem, vector angle formulas). Added separator for post-midterm-3 material. Clarified how to read off values from sine graph. Added useful info for inverse trig functions.
  - Apr 4, 2022: Added information on the problems of evaluating arctrig(trig()). Added formulas for how Nagy does this type of problem. Added more about vector geometry (unit direction vector, vector magnitude, deconstruction and reconstruction). Added material for hw 8 (orthogonality, projection, area of parallelogram and triangle, law of sines, law of cosines, general triangle solving)
  - Apr 18, 2022: Added Triangle Area formulas (SAS and Heron's)
  - Apr 26, 2022: Added section on formula combining sine and cosine of same frequency. Added warning on the $\pm$ in the half-angle formulas. Edited sum-to-product formulas to make things less error prone.
  - May 3, 2022: Added material on complex numbers (Converting between polar and cartesian, De Moivre's formula, roots of complex numbers)

Other Resources

Paul Dawkins (Lamar U) > Cheatsheets
- Has algebra, trig
Tyler Wallace's Beginning and Intermediate Algebra textbook here
- Has good problems, and many solutions