Trigonometric Functions of an Acute Angle • Section 1.2 9 are equal and the ratios of the corresponding sides are equal. In fact, we know that com-mon ratio: the sides of △ ABC are approximately 2.54 times longer than the corresponding sides of △ A ′ B ′ C ′ . So when the American student calculates sin A and the German student calculates sin A ′ , they get the same answer: 3 △ ABC ∼ △ A ′ B ′ C ′ ⇒ BC B ′ C ′ = AB A ′ B ′ ⇒ BC AB = B ′ C ′ A ′ B ′ ⇒ sin A = sin A ′ Likewise, the other values of the trigonometric functions of A and A ′ are the same. In fact, our argument was general enough to work with any similar right triangles. This leads us to the following conclusion: When calculating the trigonometric functions of an acute angle A , you may use any right triangle which has A as one of the angles. Since we deFned the trigonometric functions in terms of ratios of sides, you can think of the units of measurement for those sides as canceling out in those ratios. This means
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This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.