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MATH 141 – GOODIES FOR MIDTERM 4

FREE ONLINE GRAPHERS!

Try these graphing links:




https://www.desmos.com

(Use shift-6 “^” for exponentiation.)

(Put restrictions in { }.)




https://www.geogebra.org

(This has more with 3D graphing.  Try entering z = x^2 + y^2 and x^2 + y^2 + z^2 = 1)

 




5.1, 5.4/5.5: TRIG IDENTITIES

 

Basic Trig IDs

http://www.kkuniyuk.com/TrigBasicIDsAnyClass.pdf

 

Advanced Trig IDs

http://www.kkuniyuk.com/M1410504Handout.pdf

 

Trig cheat sheet by Paul Dawkins

https://tutorial.math.lamar.edu/pdf/trig_cheat_sheet.pdf

 

 

5.1, Part F – better solution

http://www.kkuniyuk.com/PrecalcBook/Mid4p1is0501F.pdf

 

5.2, Part A – better solution (Method 4)

http://www.kkuniyuk.com/PrecalcBook/Mid4p2is0502method4.pdf

 

5.3, Part E – (Desmos)

http://www.kkuniyuk.com/PrecalcBook/Mid4p3is0503sinx.png

            and

http://www.kkuniyuk.com/PrecalcBook/Mid4p4is0503sin4x.png

 

5.4, Part B – better solution (Page 5.46)

http://www.kkuniyuk.com/PrecalcBook/Mid4p5is0504DoubleAngle.pdf

 

5.4: Solution to Homework, #11

http://www.kkuniyuk.com/PrecalcBook/Mid4p6is0504CosineTo4th.pdf

 

 

6.5: TRIG AND IMAGINARY NUMBERS; LOOKING AT COMPLEX NUMBERS (OPTIONAL)

 

• KHAN ACADEMY ON EULER FORMULA.

(Do you have emotion?)

https://www.youtube.com/watch?v=mgNtPOgFje0

• Maclaurin polynomial approximations for y = cos(x); Desmos

http://www.kkuniyuk.com/PrecalcBook/Mid4p7is0605CosineMaclaurin.png

 

• Euler’s Identity; from Art of Mathematics

http://www.kkuniyuk.com/PrecalcBook/Mid4p8is0605EulerIdentity.png

 

• i to the i is real; from Art of Mathematics

http://www.kkuniyuk.com/PrecalcBook/Mid4p9is0605iToTheI.png

 

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