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Loyola University Chicago

Mathematics and Statistics

MATH 118: Precalculus

Credit Hours



Math Placement Test or MATH 117


Exponential and logarithmic functions. Trigonometric functions, trigonometric identities and equations. Law of sines, law of cosines, area problems, and Heron's formula. The complex plane and DeMoivre's theorem. Vectors and parametric equations. Polar coordinates. Mathematical induction. Review of conic sections. Optimization problems. Gaussian elimination, partial fractions. Word problems emphasized throughout the course.

See Course Page for additional resources.


S. Axler, Algebra and Trigonometry (packaged with WileyPLUS), 1st edition. Wiley, Hoboken (2012).
ISBN: 978-1118-08841-8.

Common Syllabus for MATH 118

Review. Prerequisite Material from MATH 117 [1.5 Weeks]
Quick review of algebra, lines, circles, quadratic expressions, and functions, followed by a more comprehensive review of the definitions and properties of exponential functions and logarithms. Exponential growth modeling can be covered lightly.

Chapter 8. Sequences, Series, and Limits [2 Weeks]

   8.1 – Sequences: definition of sequence, arithmetic/geometric sequences, recursively defined sequences.
   8.2 – Series: sums of sequences, definition of series, arithmetic/geometric series. Emphasize: summation notation. Binomial theorem is optional.
   8.3 – Limits: introduction to limits, infinite series, decimals as series, special series. 

Chapter 9. Trigonometric Functions [3 Weeks]
   9.1 – The unit circle: equation of unit circle, angles, negative angles, angles greater than 360 degrees, arc length, special points on unit circle.
   9.2 – Radians: motivation of radians, radius corresponding to an angle, arc length revisited, area of slices, special points on unit circle revisited.
   9.3 – Cosine and sine: definition of cosine and sine, signs of cosine and sine, pythagorean identity, graphs of cosine and sine.
   9.4 – More trigonometric functions: tangent, sign of tangent, connections between cosine, sine, and tangent, graph of tangent, definitions of cotangent, secant, cosecant.
   9.5 – Trigonometry in right triangles: definition of trigonometric functions via right triangles, two sides of a right triangle, one side and one angle of a right triangle
   9.6 – Trigonometric identities: relationship between cosine, sine, tangent, identities for negative angles, identities involving pi/2, identities involving multiples of pi 

Chapter 10. Trigonometric Algebra and Geometry [3 Weeks]
   10.1 – Inverse trigonometric functions: arccosine, arcsine, and arctangent functions. 
   10.2 (Optional) – Inverse trigonometric identities, graphical and algebraic approach to evaluation at –t
   10.3 – Using trigonometry to compute area: area of triangle/parallelogram via trigonometry, ambiguous angles, areas of polygons, trigonometric approximations.
   10.4 – Law of Sines and Law of Cosines: statement and uses of laws of sines/cosines, when to use which law.
   10.5 – Double-Angle and Half-Angle Formulas: sine/cosine double-angle and half-angle formulas. The corresponding formulas for tangent are optional.
   10.6 – Addition and subtraction formulas: sine/cosine/ sum and difference formulas. The corresponding formulas for tangent are optional.  

Chapter 11. Applications of Trigonometry [2.5 Weeks]
Suggestion: If time is short, 11.1 is optional. Focus on 11.2, 11.3, and 11.5.
Suggestion: Quickly review Chapter 3, Section 2 before covering 11.2
   11.1 (Optional) – Parametric curves: curves in the plane, inverse functions as parametric curves, shifts/flips of parametric curves. Stretches of parametric curves is optional.
   11.2 – Transformations of trigonometric functions: amplitude, period, phase shift, modeling periodic phenomena, modeling with data.
   11.3 Polar Coordinates: Definition of polar coordinates, conversion between polar/rectangular coordinates, graphs of circles and rays. Other polar graphs are optional.
   11.4 (Optional) – Algebraic and geometric introduction to vectors, addition and subtraction, scalar multiplication, dot product.
   11.5 – The complex plane: complex numbers as points in the plane, geometric interpretation of multiplication/division of complex numbers, De Moivre's theorem, finding complex roots.


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