UWO calculus 1501.pdf - Trigonometric Functions...

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Unformatted text preview: Trigonometric Functions Trigonometric Functions January 21, 2019 1 Trigonometric functions In this course Calc1501, the trigonometric functions are not part of the course outline, however, they appear almost everywhere in this course, so it is really necessary to remember those trigonometric functions. And the good news is that, instead of remembering so many formulas one by one, you only need to keep this hexagon diagram in your mind: sin θ cos θ 1 tan θ sec θ cot θ csc θ First let’s look at the three dark tirangles. In each dark triangle, the sum of the square of top 2 vertices is equal to the bottom vertex square, namely, sin2 θ + cos2 θ = 1; tan2 θ + 1 = sec2 θ; 2 (1) 2 1 + cot θ = csc θ. Secondly, the product of each pair of the diagonal vertices is equal to 1, namely, sin θ · csc θ = 1; cos θ · sec θ = 1; (2) tan θ · cot θ = 1. Finally, for each of the 6 vertices, it is equal to the product of its 2 neighbor vertices, namely, sin θ · cot θ = cos θ; cos θ · csc θ = cot θ; cot θ · sec θ = csc θ; csc θ · tan θ = sec θ; sec θ · sin θ = tan θ; tan θ · cos θ = sin θ. 1 (3) ...
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  • Winter '10
  • Shafikov
  • Uwo, English-language films, Summation, Binary relation, Cartesian product, tan θ, Calculus 1501

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