(1) Solving Trigonometric Equations
Solving Trigonometric Equations (page 1 of 2) Solving trig equations use both the reference angles you've memorized and a lot of the algebra you've learned. Be prepared to need to think! Solve sin(x) + 2 = 3 for 0° < x < 360° Just as with linear equations, I'll first isolate the variable-containing term: sin(x) + 2 = 3 sin(x) = 1
Lesson HOW TO - Solve Trigonometric equations
Introduction The solution of trigonometric equations is one topic that students have particular problems with. There are a few reasons for this: 1. there is usually a simplify part first that requires use of some TRIG identities. 2. there is the use of RADIANS rather than degrees, for which some students are not at ease with. 3. there is the repetitive aspect of TRIG functions that students find bewildering. All in all, a potentially daunting topic. To be honest though, there is nothing that you need fear here, so long as you take it methodically and slowly.
Graphing Trigonometric Functions
Graphing Trigonometric Functions (page 1 of 3) Sections: Introduction, Examples with amplitude and vertical shift, Example with phase shift You've already learned the basic trig graphs. But just as you could make the basic quadratic x2, more complicated, such as –(x + 5)2 – 3, so also trig graphs can be made more complicated. We can transform and translate trig functions, just like you transformed and translated other functions in algebra.
(3) Graphing Trigonometric Functions
Graphs of trigonometric functions look a little crazy at first, especially if you're expecting to find more triangles. They aren't too bad, though, once we get the hang of them. Let's start by looking at a graph of a basic sine function, y = sin x:
(4) The Key Features of the Trig Graphs (Part 1)
In this section we will summarize what you have probably already discovered from generating the graphs of the trigonometric functions. However, we will use some important terminology that will help us to describe the features of trig functions and also prepare the way to look at more complicated trig functions. We will now introduce the definition of two important concepts that help to describe the key features of the functions of sine, cosine and tangent. 1. Period
Amplitude, Period, Phase Shift and Frequency
Some functions (like Sine and Cosine) repeat forever and are called Periodic Functions. The Period is the length from one peak to the next (or from any point to the next matching point): The Amplitude is the height from the center line to the peak (or to the trough).
Algebra/Trig Review - Solving Trig Equations
Solve the following trig equations. For those without intervals listed find ALL possible solutions. For those with intervals listed find only the solutions that fall in those intervals.
(5) The Change-of-Base Formula
The Change-of-Base Formula (page 5 of 5) Sections: Basic log rules, Expanding, Simplifying, Trick questions, Change-of-Base formula There is one other log "rule", but it's more of a formula than a rule. You may have noticed that your calculator only has keys for figuring the values for the common (base-10) log and the natural (base-e) log, but no other bases. Some students try to get around this by "evaluating" something like "log3(6)" with the following keystrokes:
Algebra - Symmetry
Example 1 Determine the symmetry of each of the following equations. (a) [Solution] (b)
(4) (ii) Proofs of Logarithm Properties
OML Search In these lessons, we will look at the four properties of logarithms and their proofs. They are the product rule, quotient rule, power rule and change of base rule.
Symmetry and Graphing
Symmetry and Graphing (page 3 of 3) Sections: Symmetry about an axis, Symmetry about a point, Symmetry and graphing Symmetry is more of a geometrical than an algebraic concept, but the subject of symmetry does come up in a couple of algebraic contexts. For instance, when you're graphing quadratics, you may be asked for the parabola's axis of symmetry. This is usually just the vertical line x = h, where "h" is the x-coordinate of the vertex, (h, k). That is, a parabola's axis of symmetry is usually just the vertical line through its vertex.
