MATH& 142
PreCalculus II
LEARNING OUTCOMES
Upon successful completion of Math& 142 the student
should be able to:
- Measure angles in
degrees and radians and convert from one system to the other.
- 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.
- Define tangent,
cotangent, secant, and cosecant in terms of sine and cosine.
- State and use the fundamental
identities relating the trigonometric functions.
- Solve right triangle
application problems.
- Graph sine and
cosine functions using amplitude, period, vertical shift and phase
shifts (graph tangent,
cotangent, secant and cosecant).
- Use a graphing
calculator to create graphs of trigonometric functions and combinations of
trigonometric functions.
- Use sine and cosine
functions to model simple harmonic motion.
- Define and graph
inverse trigonometric functions.
- Solve trigonometric
equations by hand and using calculators (and extend calculator results to
additional solutions).
- Verify trigonometric
identities and find counterexamples to false Òidentities.Ó
- Use a variety of
trigonometric identities (sum, difference, double angle, half angle, etc.)
- Use the laws of
sines and cosines to solve non-right triangles and applications.
- 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.
- Calculate the dot
product of two vectors and use it to find the angle between them.
- Calculate and sketch
the projection of a vector onto a vector.
- Plot points and
graph functions given by
parametric equations by hand and using a calculator.
- Plot points and
graph functions in polar coordinates by hand and using a calculator.
- Define and graph and
list some reflection properties of parabolas, ellipses and hyperbolas.
- Use the listed tools
to solve multi-step problems and applications.