Project#3 - Project for college trigonometry. PDF

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Project for college trigonometry....

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MAC1114 — College Trigonometry — Project 3 Part I – Proofs and Derivations θ1 θ2 cos θ +i sin cos θ ¿ 1. Given two complex numbers and show that 1 2 +i sin ¿ z 1=r 1 ¿ z 2=r 2 ¿ θ1 ¿ θ1 (¿−θ2 ) (−θ2 ¿ )+ isin ¿ cos ¿ z1 r1 = ¿ z2 r2 z 1 r 1 (cos θ1 +i sin θ 1) = z 2 r 2 (cos θ2 +i sin θ 2) r r (¿ ¿ 2(cos θ 2+ isin θ2 ))(r 2(cos θ2−i sin θ2)) (¿ ¿ 1(cos θ 1+ isin θ1 ))( r 2(cos θ2−i sin θ2)) ¿ ¿¿

r 2 (¿¿ 2) (cos ( θ2 −θ2) +isin ( θ 2−θ2 ) ) r 1 r 2 (cos ( θ1−θ 2 )+ isin (θ1 −θ2 )) ¿ ¿ ¿

r 1(cos ( θ1−θ 2 ) +isin ( θ 1−θ2 ) ) r 2 (cos 0+isin 0)

z1 r1 = (cos ( θ1−θ 2 )+ isin (θ1 −θ2 )) z2 r2 (−θ ) 2. Show that the product of cos (−θ ) +i sin ¿ and z=r (cos θ +isin θ ) z=r ¿ square of the modulus. [ r (cos (−θ )+ isin (−θ ) ) ]∗[ r ( cosθ +isin θ ) ] ¿ r 2∗[cos ( θ−θ)+isin (θ−θ ) ] ¿ r 2 (cos 0+ isin 0) ¿ r2

is equal to the

[ r (cos (−θ )+ isin (−θ ) ) ]∗[ r ( cosθ +isin θ ) ]=r 2 Part II – Conceptual Questions 1. True or False? Explain your answer. If a triangle contains an obtuse angle, then it must be oblique. True. An oblique triangle is a triangle without a right angle. If one angle is greater than 90 degrees then no other angle can equal 90 degrees. 2. True or False? Explain your answer. Because the sine function is an odd function, for a negative number u, sin 2u=−2 sin u cos u . False because cosine is an even function. π...