Special Right Triangle 30º- 60º- 90ºThe 30º- 60º- 90º triangle is one of two special right triangles we will be investigating. The “special” nature of these triangles is their ability to yield exact answers instead of decimal approximations when dealing …

Special Right TrianglesThere are two “special” right triangles with which you need to be familiar; the 45º- 45º- 90º triangle and the 30º- 60º- 90º triangle. The “special” nature of these triangles is their ability to yield exact answers instead of deci…

Graphs of Functions y = sin(x) and y = cos(x)Graphs of trigonometric functions can be produced in degrees or in radians. The graphs appearing here will be done in radians.Hint: When hand-drawing the graphs of sine and cosine, draw vertical dotted lines a…

Special Right Triangle 45º- 45º- 90ºThe 45º- 45º- 90º triangle is one of two special right triangles we will be investigating. The “special” nature of these triangles is their ability to yield exact answers instead of decimal approximations when dealing…

Step-by-Step Graphing of a Sinusoid of the Form y = A sin(B(x – C)) + DSinusoid: y =A sin (B(x-C))+DOf course, any graphing utility can produce an accurate graph of a sinusoid. But how do you accomplish this task if you must graph by hand? Step-by-Step …

Working with Trig InversesWhen working with trigonometric inverse problems, remember the following information: Examples:

The Six Trigonometric Functions and Reciprocals FunctionsIn a right triangle, there are actually six possible trigonometric ratios, or functions. A Greek letter (such as theta or phi ) will now be used to represent the angle. Notice that the three new …

Trigonometric Ratios Of Complementary Angles We know Trigonometric ratios of complementary angles are pair of angles whose sum is 90° Like 40°, 50°, 60°, 30°, 20°, 70°, 15°, 75° ; etc, Formulae: sin (90° – θ) = cos θ,         cot (90° – θ) = tanθ cos (…

Using All Trigonometric IdentitiesTrigonometric Identities When simplifying expressions, or factoring expressions, look for common factors. If none exist, look for related functions from the identities that will assist in the simplification.

Absolute Value of Complex NumbersGeometrically, the absolute value of a complex number is the number’s distance from the origin in the complex plane. In the diagram at the left, the complex number 8 + 6i is plotted in the complex plane on an Argand diagr…