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• 6.1: Solving Trigonometric Equations
In Chapter 1 we were concerned only with finding a single solution (say, between $$0^◦\text{ and }90^◦$$ ). In this section we will be concerned with finding the most general solution to such trigonometric equations.
• 6.2: Numerical Methods in Trigonometry
We were able to solve the trigonometric equations in the previous section fairly easily, which in general is not the case. Instead, we have to resort to numerical methods, which provide ways of getting successively better approximations to the actual solution(s) to within any desired degree of accuracy.
• 6.3: Complex Numbers
There is no real number $$x$$ such that $$x^ 2 = −1$$. However, it turns out to be useful to invent such a number, called the imaginary unit and denoted by the letter i.
• 6.4: Polar Coordinates
Suppose that from the point (1,0) in the xy-coordinate plane we draw a spiral around the origin, such that the distance between any two points separated by $$360^\circ$$ along the spiral is always 1, as in Figure 6.4.1. We can not express this spiral as $$y = f (x)$$ for some function $$f$$ in Cartesian coordinates, since its graph violates the vertical rule. However, this spiral would be simple to describe using the polar coordinate system.