Sinusoidal Graphs: y = A sin(B(x – C)) + DA sine wave, or sinusoid, is the graph of the sine function in trigonometry. A sinusoid is the name given to any curve that can be written in the form (A and B are positive). Sinusoids are considered to be the g…

Solving Quadratic Equations with the Quadratic FormulaThe solutions of some quadratic equations, ax2 + bx + c = 0 (a≠0) are not rational, and cannot be obtained by factoring. For such equations, the most common method of solution is the quadratic formul…

Trigonometric Identities(1) \(\tan \theta =\frac{\sin \theta }{\cos \theta }\text{ (linear)}\) Conditional trigonometrical identitiesWe have certain trigonometric identities. Like sin2 θ + cos2 θ = 1 and 1 + tan2 θ = sec2 θ etc. Such identities are id…

Law of SinesWhen you see the triangle below on the left and someone asks you to find the value of x, you immediately know how to proceed. You call upon your friend the Pythagorean Theorem because you see the right angle. But what do you do when you see t…

SequencesIn the previous lesson, we learned about pattern of numbers. In this lesson we discuss about Sequences. A sequence is an ordered list of numbers. The sum of the terms of a sequence is called a series.Each number of a sequence is called a term …

FactorialsIn mathematics, the factorial of a natural number n is the product of the positive integers less than or equal to n. This is written as n! and pronounced n factorial’. The numeric value of n! can be calculated by repeated multiplication, if n i…

Error in Differing DimensionsError increases when dimensions increase. Consider the following example:1. A student measures the side of a cube and accidentally reads a length of 5 inches, when the real length is 6 inches. Notice how the percentage of err…

Vocabulary ResourceThis is a partial listing of basic FORMAL definitions needed when working with Euclidean geometry and proofs. You need to have a thorough understanding of these terms.An acute angle is an angle whose measure is greater than 0° and less…

Absolute Value EquationsTo solve an absolute value equation, isolate the absolute value on one side of the equal sign, and establish two cases:Case 1: |a| = b set a = b Set the expression inside the absolute value symbol equal to the other given expressi…

Evaluating Rational (Fractional) ExponentsWhen asked to “evaluate” an expression, you are most likely being asked to find a numerical value.  You should not stop until you arrive at the best, and simplest, form for the answer.   Before we go any further,…