TRIGONOMETRY LESSONS
Whether needing help with trigonometry homework or reviewing for tests, Mr. X can help math students grasp all angles of Trigonometry. Our lessons are designed to reinforce the instructor's message. We also have a library of sample trigonometry problems with examples of solved problems for each trig lesson. Check out our free samples below, as well as the trigonometry curriculum.
Trigonometry Sample Lesson 1
Trigonometry Sample Lesson 2
Trigonometry Curriculum
General Topics
Title DescriptionFind Angle Θ 14022 Version E  Given a point in Cartesian Coordinates, find the angle that describes a terminal ray going through that point. We emphasize the ratios of the sides of a 30°  60°  90° triangle. 

Find Angle Θ 14022 Version F  Given a point in Cartesian Coordinates, find the angle that describes a terminal ray going through that point. We emphasize the ratios of the sides of a 30°  60°  90° triangle. 

Find Angle Θ 14022 Version G  Given a point in Cartesian Coordinates, find the angle that describes a terminal ray going through that point. We emphasize the ratios of the sides of a 30°  60°  90° triangle. 

Lesson for Problem Set 02  These problems are also found in Trig Problem Set 02. Given a value for one basic trigonometric function, solve for the other basic trig function values for the given angle. 

Play with an Identity  Let's play with a basic trigonometric identity.  
TRIG 095  Distance Formula, Pythagorean Theorem  We find the distance between two points in rectangular (or Cartesian) coordinates. We also look at the familiar Pythagorean Theorem for the relationship between sides of a right triangle. 

TRIG 096  Square Roots and Absolute Value  Square roots and absolute value are important to understand before any formal course in plane trigonometry.  
TRIG 097  Rays, Angles, Degrees, Seconds, Circumference  Rays, angles, degrees, seconds, and circumference are basic geometric concepts that are essential to learning trig.  
TRIG 098  Quadrants in Rectangular Coordinates; Axes  Mr. X, Mentor of Mathematics, prepares you for a course in trigonometry by reviewing the tenets of rectangular coordinates and the equations of lines as well as the equations of the axes themselves.  
TRIG 099  Right Triangles, Pythagorean Triples  Pythagorean relations for the sides of a right triangle are a prerequisite to any course in plane trigonometry. It is also good to be familiar with Pythagorean Triples, which are sets of three integers a, b, and c that conform to: a² + b² = c². 

TRIG 101A  Standard Position of an Angle; Theta  We define positive rotation of a ray as generating a positive angle, while clockwise rotation generates negative angles.  
TRIG 101B  The Six Basic TRIG Functions  While we have six basic trigonometric functions, in this lesson we concentrate on "the first three," namely, sine, cosine, and tangent.  
TRIG 101C  Tangent is Just Like Slope  We introduce x, y, and r around a circle centered at the origin. the radius of the circle is r, and points around the circle are the familiar (x, y). 

TRIG 101D  Reciprocal TRIG Functions  Quickly learn the pairs of reciprocal trig functions: sine and cosecant are reciprocal trig functions; cosine and secant are reciprocal trig functions; tangent and cotangent are reciprocal trig functions.  
TRIG 101E  Cofunctions  The names of the six basic trig functions make it easy to follow: sine and cosine functions are cofunctions; tangent and cotangent functions are cofunctions; secant and cosecant functions are cofunctions.  
TRIG 101F  Coterminal Angles; Values Around Unit Circle  Feel free to stop this lesson anywhere along the way to observe sine and cosine values around the Unit Circle.  
TRIG 101G  Reference Angles; Related Angles  Every angle in standard position has an associated Reference Angle (or Related Angle) that is equivalent to a firstquadrant angle. It is "the quickest way back to the xaxis." Also, standard values for standard angles (multiples of 30 degrees and 45 degrees) are noted. 

TRIG 102A  Angles of Elevation, Depression  We reference both angles of elevation and angles of depression to a horizontal line.  
TRIG 102B  Bearings and Headings  Bearings and Headings are similar concepts, both related to compass points and navigational vectors.  
TRIG 102C  Inverse TRIG Functions  Inverse TRIG functions return an angle.  
TRIG 102D  Radian Measure, Arc Length  Radians are just as good as degrees for measuring angles, and sometimes better. We develop a comfort level in expressing angles in terms of pi. 

TRIG 102E  Angular and Linear Velocity  Linear velocity and angular velocity are explained with omega, as both revolutions per unit time and radians per unit time.  
TRIG 102F  Identities and Conditional Statements  An introduction to identities, and a comparison to conditional statements that are true only under certain conditions. Basic ideas are reviewed, but the lesson ends with a serious identity appropriate for serious students of trig. 

TRIG 102G  Functions of Two Angles  We look at formulas and identities for functions of two angles, both producttosum formulas and sumtoproduct formulas.  
TRIG 103A  Oblique Triangles  Any triangle that is not a right triangle is considered an oblique triangle. The sine of an angle is equal to the sine of that angle's supplement. We also delve into the ambiguous SSA case for triangle congruence. 

TRIG 103B  Law of Sines  We use the L.O.S. to solve triangles. 

TRIG 103C  Ambiguous SSA  Given two sides of a triangle and one angle not between those sides, there are two ways, conceivably, to build that triangle. Hence, the SSA test for congruence is ambiguous. 

TRIG 103D  Law of Cosines  The Law of Cosines allows us to solve triangles. The Pythagorean relation is a special case of the L.O.C. 

TRIG 103E  Area of a Triangle  There are many ways to calculate the area of a triangle. Trigonometry helps when the altitude of the triangle is unknown. We look at Heron's (Hero's) Formula, as well as a 3x3 determinant. 

TRIG 104A  Waveform Amplitude  The amplitude of a waveform (or sinusoid) is half the distance from the highest and lowest values.  
TRIG 104B  Waveforms: Period and Compression Factor  Waveforms are changed with factors that affect period. We like the term compression factor. 

TRIG 104C  Waveforms: Phase Shift  The horizontal shift of a sinusoid or waveform is termed a phase shift.  
TRIG 104D  Waveforms: Vertical Shift  We take the vertical shift of a waveform and put it together with the previous lessons on amplitude, compression factor, and phase shift.  
TRIG 105A  Complex Numbers  After a brief description of complex number basics, we show the trigonometric form of a complex number.  
TRIG 105B  Complex Numbers Multiplied in TRIG Form  While phasor notation makes multiplication of complex numbers exceedingly simple, we look at complex multiplication algebraically, as well.  
TRIG 105C  DeMoivre's Theorem  Raising a complex number to a real power, n, is a straightforward process: the r (the radius) is raised to the power of n, but we simply insert a coefficient of n on the angle. 