## LEARN TRIGONOMETRY

Whether needing help with trigonometry homework or reviewing for tests, Mr. X can help math students grasp all angles and really learn 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. Trig lessons and problems are included with a subscription to Mr. X.
Trigonometry Sample Lesson 1
Trigonometry Sample Lesson 2
Trigonometry Sample Lesson 3

# Learn Trigonometry

Title Description
Find 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 first-quadrant angle.
It is "the quickest way back to the x-axis." 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 product-to-sum formulas and sum-to-product 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. Sample Arithmetic Problems | Math Glossary | Solving Algebra Problems | Trig Homework | Homework Help with Algebra | Learn Trigonometry | Math Glossary Geometry | Calculus Glossary