Trigonometry

A Mind-Stretching Exercise with a Stretched Cosine

(A new question of the week) A question in September, about graphing a horizontally-stretched cosine function, led to a long conversation. Between a typo in the problem and some inside-out thinking, this surprisingly non-routine problem led to some good mind-stretching! I have edited this down considerably by removing distractions from the main ideas, but it …

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Challenging Inverse Trig and Polynomial Equations

(A new question of the week) We have had a lot of interesting questions recently. This one involved inverse trigonometric equations that led to cubic and quartic equations. We’ll observe here one of the benefits of embedding the original discussion in a blog format where I can add information that will help you, the reader, …

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How Far Can I See?

We have been looking at questions about the roundness of the earth, starting with the general fact, and then the determination of the size of the earth. A very common question is about how that roundness affects what we can see, sometimes as a challenge (“If I can see this, then how can the earth …

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Oblique Triangles in Applications

Having just looked at how to solve oblique triangles, let’s look at a couple “word problems” (applications) involving such triangles. We’ll be using the Law of Sines, and also exploring alternative methods of solution. A tilted tree Let’s start with this real application from 1999: Will the Tree Hit the House? There is a tree …

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