The Latin root tactus is part of the word tangent. What does the word tangent mean?
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The figure below illustrates a connection between the two meanings of the word tangent in geometry. (IMAGE CAN'T COPY) What is the definition of tangent in terms of an acute angle of a right triangle?
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The word tangent literally means "to touch," which in mathematics we take to mean touches in only and exactly one point. In the figure, the circle has a radius of 1 and the vertical line is "tangent" to the circle at the $x$ -axis. The figure can be used to verify the Pythagorean identity for sine and cosine, as well as the ratio identity for tangent. Discuss/Explain how.
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