Technical Mathematics Part 2 TSYH 2123

Upon successful completion, the student will be able to:

Chapter 1 - Radian Measure and Rotation

• To define an angle of 1 radian.
• To determine the radian equivalent of an angle in degrees and vice versa.
• To determine the values of the trigonometric functions of angles expressed in radians.
• Given any two of the arc length, central angle and radius, to determine the third.
• To determine the area of a sector of a circle.
• To determine the area of a segment of a circle.
• To translate between linear velocity and angular velocity for a rotating body.

Chapter 2 - Graphs of Trigonometric Functions

• To plot the graph of a trigonometric function of the form y = A sin x or y = - A cos x.
• To sketch the graph of such a function.
• To identify the amplitude from the graph and from the equation of the function.
• To plot the graphs of the functions y = A sin bx, y = A cos bx.
• To sketch the graphs of these functions.
• To identify the period of the function from the graph and from the equation.
• To plot the graphs of y = A sin (bx + c) and y = A cos (bx + c).
• To sketch the graphs of these functions.
• To identify the phase displacement from the graph and from the function.
• To sketch the sine and cosine functions using the period, amplitude and phase displacement data only.
• To sketch the graph of y = tan x.
• To determine the period of the tangent function from the graph.
• To graph a function by graphing component functions and adding ordinates.
• To add two trigonometric functions perpendicularly given their parametric equations.
• To introduce the polar coordinate system as an alternative graphing model.
• To plot points in polar coordinates.
• To graph equations in polar coordinates.
• To transform polar to rectangular coordinates and vice versa.

Chapter 3 - Trigonometric Identities and Equations

• Transform trigonometric functions using the fundamental trigonometric identities.
• Transform trigonometric functions using the compound angle formulae.
• Transform trigonometric functions using the double angle formulae.
• Transform trigonometric functions using the half angle formulae.
• Solve trigonometric equations using as required, appropriate trigonometric identities.
• Identify the different ways of writing inverse trigonometric functions.
• Sketch the graph of the inverse function.

Chapter 4 - Functional Variation

• Identify 'varies directly as or directly proportional to' functional relationships.
• Solve direct variation problems.
• Identify 'power function' functional relationships.
• Distinguish between the graphs of power functions for various values of the exponent.
• Solve power function problems.
• Distinguish 'inverse variation' functional relationships.
• Solve inverse variation problems.
• Distinguish 'joint variation' functional relationships.
• Solve joint variation problems.

Chapter 5 - Exponential and Logarithmic Functions

• Identify an exponential function.
• Graph the exponential function.
• Distinguish between exponential growth and decay functions.
• Solve problems involving the exponential function.
• Define the logarithmic function.
• Convert between logarithmic and exponential form.
• Graph the logarithmic function.
• Solve logarithm equations.
• Transform the logarithms of products, quotients and exponentiations into the sums, differences and multiples of logarithms and vice versa.
• Transform logarithms in one base to equivalent logarithms in another base.
• Solve exponential equations using logarithms.
• Solve logarithmic equations.

Chapter 6 - Inequalities

• Establish some fundamental definitions for inequalities.
• Solve inequalities graphically.
• Write the absolute value inequality as an equivalent statement without the absolute value signs.
• Solve an absolute value inequality.

Chapter 7 - The Straight Line

• Compute the length of a line segment connecting two points.
• Determine the slope of a line passing through two points.
• Determine the slope relationship between parallel and perpendicular lines.
• Establish the equation of a straight line in the following forms:
• Slope and intercept
• General
• Point slope
• Two point
• Intercept.

Chapter 8 - Empirical Equations

• Establish the functional relationship given data which yield a straight line when plotted on regular graph paper.
• Establish the functional relationship given data which yield a straight line when plotted on log-log paper.
• Establish the functional relationship given data which yield a straight line when plotted on semilog graph paper.

Effective as of Fall 2003