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.

Sketching the graph of a given trigonometric function
The graphs of the three major functions are very important and you need to learn the characteristics of each. The sine function This graph is continuous (there are no breaks).
Solving Simple Trigonometric Equations
Solving General Trigonometric Equations Objective: Given a trigonometric equation of one of the following forms: A * sin (ax+b) = k A * cos (ax+b) = k A * tan (ax+b) = k A * cot (ax+b) = k A * sec (ax+b) = k A * csc (ax+b) = k where k is some constant, A, a and b are real numbers, the learner will:

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.

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

4. Graphs of tan, cot, sec and csc
by M. Bourne The graphs of tanx, cotx, secx and cscx are not as common as the sine and cosine curves that we met earlier in this chapter. However, they do occur in engineering and science problems. They are interesting curves because they have discontinuities.
SOLVING TRIGONOMETRIC EQUATIONS
Note: If you would like a review of trigonometry, click on trigonometry. Example 1: Solve for x in the following equation. There are an infinite number of solutions to this problem. First isolate the cosine term. To solve for x, we have to isolate x. How do we isolate the x?

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).
Trigonometric Equations
Remember to first solve for the trig function and then solve for the angle value. Solution: If there is more than one trig function in the equation, identities are needed to reduce the equation to a single function for solving. Example: Solution: There are trig equations, just like there are normal equations, where factoring does not work!!