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Unformatted text preview: Math 17 TWHFW7 1 st Sem AY 201112 Exercise Set 5 Key October 6, 2011 I. 1. True. 2. False. Consider x = 1 → y = π 2 . 3. False. Consider 0. 4. True. SSS with all lengths positive and √ 5 < 4 − √ 3. 5. True. Arccot , arctan and sin all have D = R . R sin = [ − 1 , 1] ⊂ D sec . 6. False. SSA, γ is acute, lengths positive and b sin γ = 1 . 5 < c = 2 < b = 3 → 2 △ s formed. 7. False. Consider 0. 8. True. 9. False. 10. False. Consider 2 cis 0. II. 1. Right triangle. Both leg lengths positive. → 1 △ c = radicalBig (2 √ 3 − 3) 2 + ( radicalbig 7 − 4 √ 3) 2 = radicalbig 21 − 12 √ 3 + 7 − 4 √ 3 = radicalbig 28 − 16 √ 3 c = 2 radicalBig 7 − 4 √ 3 sin β = b c = 1 2 → β = 30 ◦ → α = 60 ◦ 2. SSS with all lengths positive. → 1 △ Note that 2 √ 2 + 2 √ 6 is largest. a 2 = b 2 + c 2 − 2 bc cos α cos α = (2 √ 2 + 2 √ 6) 2 + (3 √ 2) 2 − (4) 2 2(2 √ 2 + 2 √ 6)(4 √ 2) = (32 + 16 √ 3) + 32 − 16 2(16 + 16 √ 3) = 16(3 +...
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This note was uploaded on 11/09/2011 for the course MATH 17 taught by Professor Aaronjamesporlante during the Summer '11 term at University of the Philippines Diliman.
 Summer '11
 AaronJamesPorlante
 Math, Algebra

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