The discussion focuses on solving trigonometric equations, specifically how to determine the number of solutions within the interval [0, 2π]. When given sec(x) = 2, the corresponding cosine value is cos(x) = 1/2, which yields two solutions. Conversely, for sec(x) = -1, the equivalent cosine equation cos(x) = -1 has only one solution. Utilizing the unit circle is emphasized as a crucial method for visualizing and solving these equations.
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A solution of an equation is a number that makes the equation a true statement. For example, the equation x2 - 3x + 2 = 0 is true only for x = 1 or x = 2. Any other value of x gives a value on the left side different from zero.Tyrion101 said:I'm thinking I may not understand what is a possible solution of a problem and what not.
Yes, that's right.Tyrion101 said:The interval for all of my problems is 0 to 2pi. So I suppose that if my answer was Sec=2, that I'd convert it to Cos, then it would be all of the angles that x = 1/2.
Let's look at the equation sec(x) = 2 first before going off to another problem. Within the interval [0, ##2\pi##], how many numbers are there for which cos(x) = 1/2? Looking at the unit circle is very helpful.Tyrion101 said:I think I have this much right, my confusion is when there are two answers, such as the one listed above, and say sec = -1. What do I do here?