COURSE PROCEDURE FOR TRIGONOMETR

COURSE PROCEDURE FOR TRIGONOMETRY

Chapter 4 APPLICATIONS OF TRIGONOMETRIC FUNCTIONS Section: 4.1 – 4.5
Outcomes: The student will be able to use Law of Sines and Law of Cosines; find area of oblique triangles;
re present vectors ; perform mathematical operations on vectors; find direction of vectors; find dot
products of two vectors and use properties of the dot product.

A	B	C	D	F	N		Specific Competencies Demonstrate the ability to:
						4.1	Find the value of trigonometric functions of an acute angle using right triangles.
						4.1	Use the complementary angle theorem.
						4.1	Solve right triangles.
						4.1	Solve applied problems.
						4.2	Solve SAA or ASA triangles.
						4.2	Solve SSA triangles.
						4.2	Solve applied problems.
						4.3	Solve SAS triangles.
						4.3	Solve SSS triangles.
						4.3	Solve applied problems.
						4.4	Find the area of SAS triangles.
						4.4	Find the area of SSS triangles.
						4.5	Find an equation for an object in simple harmonic motion.
						4.5	Analyze simple harmonic motion.
						4.5	Analyze an object in damped motion.
						4.5	Graph the sum of two functions

Chapter 5 POLAR COORDINATES; VECTORY Section: 5.1 – 5.7
Outcomes: The student should be able to perform operations with complex numbers ; find the zeros of a
function ; multiply and divide complex numbers written in trigonometric form; find powers
and nth roots of complex numbers.

A	B	C	D	F	N		Specific Competencies Demonstrate the ability to:
						5.1	Plot points using polar coordinates.
						5.1	Convert from polar coordinates to rectangular coordinates.
						5.1	Convert from rectangular coordinates to polar coordinates.
						5.1	Transform equations from polar to rectangular form.
						5.2	Graph and identify polar equations by converting to rectangular equations.
						5.2	Test polar equations for symmetry.
						5.2	Graph polar equations by plotting points.
						5.3	Convert a complex number from rectangular form to polar form.
						5.3	Plot points in the complex plane.
						5.3	Find products and quotients of complex numbers in polar form.
						5.3	Use De Moivre’s Theorem.
						5.3	Find complex roots.
						5.4	Graph vectors.
						5.4	Find a position vector
						5.4	Add and subtract vectors.
						5.4	Find a scalar multiple and the magnitude of a vector.
						5.4	Find a unit vector.
						5.4	Find a vector from its direction and magnitude.
						5.4	Analyze objects in static equilibrium.
						5.5	Find the dot product of two vectors.
						5.5	Find the angle between two vectors.
						5.5	De termine whether two vectors are parallel.
						5.5	Determine whether two vectors are orthogonal.
						5.5	Decompose a vector into two orthogonal vectors.
						5.5	Compute work.
						5.6	Find the distance between two points in space.
						5.6	Find position vectors in space.
						5.6	Perform operations on vectors in space.
						5.6	Find the dot product.
						5.6	Find the angle between two vectors.
						5.6	Find the direction angles of a vector.
						5.7	Find the cross product of two vectors
						5.7	Know algebraic properties of the cross product.
						5.7	Know geometric properties of the cross product.
						5.7	Find a vector orthogonal to two given vectors.
						5.7	Find the area of a parallelogram.

Chapter 6 ANALYTIC GEOMETRY Section: 6.1 – 6.7
Outcomes: The student should be able to write the standard forms of the equations of basic conics, analyze and
sketch parabolas, ellipses, and hyperbolas, and eliminate the x y-term in equations of conics and classify
conics.

A	B	C	D	F	N		Specific Competencies Demonstrate the ability to:
						6.1	Know the names of the conics
						6.2	Analyze parabolas with vertex at the origin.
						6.2	Analyze parabolas with vertex at (h, k).
						6.2	Solve applied problems involving parabolas.
						6.3	Analyze ellipses with center at the origin.
						6.3	Analyze ellipses with center at (h, k).
						6.3	Solve applied problems involving ellipses.
						6.4	Analyze hyperbolas with center at the origin.
						6.4	Find the asymptotes of a hyperbola.
						6.4	Work with ellipses with center at (h, k).
						6.4	Solve applied problems involving hyperbolas.
						6.5	Identify a conic.
						6.5	Use a rotation of axes to transform equations.
						6.5	Analyze an equation using a rotation of axes.
						6.5	Identify conics without a rotation of axes.
						6.6	Analyze and graph polar equations of conics.
						6.6	Convert the polar equation of a conic to a rectangular equation.
						6.7	Graph parametric equations.
						6.7	Find a rectangular equation for a curve defined parametrically.
						6.7	Use time as a parameter in parametric equations
						6.7	Find parametric equations for curves defined by rectangular equations.

Chapter 7 EXPONENTIAL AND LOGARITHMIC FUNCTIONS Section: 7.1 – 7.7
Outcomes: The student should be able to recognize, evaluate, and graph exponential and logarithmic functions;
rewrite logarithmic functions with different bases; use properties of logarithms to evaluate, rewrite,
expand, and condense logarithmic expressions; solve logarithmic and exponential equations; use
different logarithmic and exponential formulas to solve real-life problems; fit exponential and logarithmic
models to sets of data.

A	B	C	D	F	N		Specific Competencies Demonstrate the ability to:
						*7.1	Evaluate exponential functions.
						*7.1	Graph exponential functions.
						*7.1	Define the number e.
						*7.1	Solve exponential equations.
						*7.2	Change exponential expressions to logarithmic expressions and logarithmic expressions to exponential expressions.
						*7.2	Evaluate logarithmic functions.
						*7.2	Determine the domain of a logarithmic function.
						*7.2	Graph logarithmic functions.
						*7.2	Solve logarithmic equations.
						*7.3	Work with the properties of logarithms.
						*7.3	Write a logarithmic expression as a sum or difference of logarithms.
						*7.3	Write a logarithmic expression as a single logarithm.
						*7.3	Evaluate logarithms whose base is neither 10 nor e.
						*7.4	Solve logarithmic equations.
						*7.4	Solve exponential equations.
						*7.4	Solve logarithmic and exponential equations using a graphing utility.
						*7.5	Determine the future value of a lump sum of money.
						*7.5	Calculate effective rates of return.
						*7.5	Determine the present value of a lump sum of money.
						*7.5	Determine the rate of interest or time required to double a lump sum of money.
						*7.6	Find equations of populations that obey the law of uninhibited growth.
						*7.6	Find equations of populations that obey the law of decay.
						*7.6	Use Newton’s Law of Cooling.
						*7.6	Use logistic models.
						*7.7	Use a graphing utility to fit an exponential function to data.
						*7.7	Use a graphing utility to fit a logarithmic function to data.
						*7.7	Use a graphing utility to fit a logistic function to data.

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