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Why the relationship of sine and cosine holds for complementary angles.?
Wiki User
∙ 9y ago
The answer depends on how sine and cosine are defined: as ratios in right angled triangles, as infinite series or some other way (there are many). The explanation is easiest for definitions based on right angled triangles. Since this browser does not allow graphics, the explanation will be simpler to follow if you just sketch a rough triangle.
Suppose you have triangle ABC which is right angled at C.
Then, since angle A + angle B + angle C = 180 degrees,
angle A + angle B = 90 deg.
That is, A and B are complementary angles.
Now consider the ratio of the sides BC/AB.
AB is the hypotenuse of the triangle.
From the perspective of angle A, BC is the opposite side so the above ratio is sin(A).
From the perspective of angle B, BC is the adjacent side so the above ratio is cos(B).
Thus sin(A) = cos(B).
Similarly, if you consider AC/AB you can show that cos(A) = sin(B).
Wiki User
∙ 9y ago
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