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# L27 - Lecture 27 Part I Section 4.3 Right Triangle...

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Lecture 27, Part I: Section 4.3 Right Triangle Trigonometry Def. Let u1D703 be an acute angle of a right triangle. The six trigonometric functions of the angle u1D703 are defined as follows. sin u1D703 = csc u1D703 = cos u1D703 = sec u1D703 = tan u1D703 = cot u1D703 =

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ex. Find the values of the six trigonometric functions of u1D703 . 2 4 ex. If cos u1D703 = 3 4 , sketch a right triangle with acute angle u1D703 , and find the other values of the five trigono- metric functions of u1D703 .
Theorem: Cofunctions of complementary angles are equal. That is, sin(90 u1D703 ) = cos u1D703 cos(90 u1D703 ) = sin u1D703 tan(90 u1D703 ) = cot u1D703 cot(90 u1D703 ) = tan u1D703 sec(90 u1D703 ) = csc u1D703 csc(90 u1D703 ) = sec u1D703 a b c θ ex. Evaulate: 1) sin 36 cos 54 2) tan 56 cot 34

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Trigonometric Identities 1. Reciprocal Identities sin u1D703 = 1 csc u1D703 csc u1D703 = 1 sin u1D703 cos u1D703 = 1 sec u1D703 sec u1D703 = 1 cos u1D703 tan u1D703 = 1 cot u1D703 cot u1D703 = 1 tan u1D703 2. Quotient Identities tan u1D703 = sin u1D703 cos u1D703 cot u1D703 = cos u1D703 sin u1D703 3. Pythagorean Identities
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