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:
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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