Trigonometry

A Tunnel Through the Earth

I have a very short problem this week: How deep will you go if you dig a straight tunnel through the earth, how long will it be, and what angle do you have to start at?

Two Sinusoidal Models

(A new question of the week) Two recent questions involved using trigonometric functions to model real-life (or nearly so) situations, one about breathing, the other about a Ferris wheel. Both can be done by writing a sinusoidal function; the second can be done in other interesting ways as well.

Trig Identities: Where’d That Come From?

(A new question of the week) Proving a trigonometric identity can be a challenge; sometimes even when we read someone else’s proof, we can fail to see how they came up with a seemingly magical step. We’ll look at two such identities here, and consider how to bridge a gap when we are stuck.

Sines Without Right Triangles

(A new question of the week) A recent question dealt with an apparent conflict between the right-triangle definition of sines and cosines, and the unit-circle definition, pertaining to multiples of 90° (angles on the axes). This provides an opportunity to look closely at the relationship between those two definitions. Two definitions Recall that the right-triangle …

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