MATH& 142

PreCalculus II

LEARNING OUTCOMES

 

Upon successful completion of Math& 142 the student should be able to:

 

  1. Measure angles in degrees and radians and convert from one system to the other.

 

  1. State the definitions of sine and cosine on the unit circle and for right triangles and give the values of sine and cosine at the ÒspecialÓ angles on the unit circle.

 

  1. Define tangent, cotangent, secant, and cosecant in terms of sine and cosine.

 

  1. State and use the fundamental identities relating the trigonometric functions.

 

  1. Solve right triangle application problems.

 

  1. Graph sine and cosine functions using amplitude, period, vertical shift and phase shifts  (graph tangent, cotangent, secant and cosecant).

 

  1. Use a graphing calculator to create graphs of trigonometric functions and combinations of trigonometric functions.

 

  1. Use sine and cosine functions to model simple harmonic motion.

 

  1. Define and graph inverse trigonometric functions.

 

  1. Solve trigonometric equations by hand and using calculators (and extend calculator results to additional solutions).

 

  1. Verify trigonometric identities and find counterexamples to false Òidentities.Ó

 

  1. Use a variety of trigonometric identities (sum, difference, double angle, half angle, etc.)

 

  1. Use the laws of sines and cosines to solve non-right triangles and applications.

 

  1. Define and graph vectors in 2-D and 3-D and use the properties of vectors to add, subtract and stretch vectors and solve applications.

 

  1. Calculate the dot product of two vectors and use it to find the angle between them.

 

  1. Calculate and sketch the projection of a vector onto a vector.

 

  1. Plot points and graph functions given by  parametric equations by hand and using a calculator.

 

  1. Plot points and graph functions in polar coordinates by hand and using a calculator.

 

  1. Define and graph and list some reflection properties of parabolas, ellipses and hyperbolas.

 

  1. Use the listed tools to solve multi-step problems and applications.