 # 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 Now I'll use the reference angles I've memorized: x = 90° Solve tan2(x) + 3 = 0 for 0° < x < 360° There's the temptation to quickly recall that the tangent of 60° involves the square root of 3 and slap down an answer, but this equation doesn't actually have a solution: tan2(x) = –3 How can the square of a trig function evaluate to a negative number? no solution Solve on 0° < x < 360° To solve this, I need to do some simple factoring: Now that I've done the algebra, I can do the trig. x = 30°, 90°, 270°, 330° Copyright © Elizabeth Stapel 2010-2011 All Rights Reserved Solve sin2(x) – sin(x) = 2 on 0° < x < 360° Only one of the factor solutions is sensible. x = 270° Hmm...

Amplitude and Period Amplitude and Period Learning Objective(s) · Understand amplitude and period. · Graph the sine function with changes in amplitude and period. · Graph the cosine function with changes in amplitude and period. (2) 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).

Properties of The Six Trigonometric Functions The properties of the 6 trigonometric functions: sin (x), cos (x), tan(x), cot (x), sec (x) and csc (x) are discussed. These include the graph, domain, range, asymptotes (if any), symmetry, x and y intercepts and maximum and minimum points. Sine Function : f(x) = sin (x) Graph

A-level Maths Trigonometry Revision - Graphs of trigonometric functions 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). 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. (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

Graphing Trigonometric Functions Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift. Find the amplitude Amplitude Find the period using the formula More Steps The period of the function can be calculated using 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. 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. 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!!

Trigonometric and Geometric Conversions, Sin(A + B), Sin(A - B), Sin(AB) Ratios for sum angles As the examples showed, sometimes we need angles other than 0, 30, 45, 60, and 90 degrees. In this chapter you need to learn two things: 1. Sin(A + B) is not equal to sin A + sin B. It doesn't work like removing the parentheses in algebra. 2. The formula for what sin(A + B) does equal. The Graphs of Sine and Cosine A 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).

Basic Trigonometric Graphs Trigonometric Functions and Their Graphs: The Sine and Cosine (page 1 of 3) Sections: The sine and cosine, The tangent, The co-functions At first, trig ratios related only to right triangles. Then you learned how to find ratios for any angle, using all four quadrants. Then you learned about the unit circle, in which the value of the hypotenuse was always r = 1 so that sin(θ) = y and cos(θ) = x. In other words, you progressed from geometrical figures to a situation in which there was just one input (one angle measure, instead of three sides and an angle) leading to one output (the value of the trig ratio).

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