✔ 最佳答案
1.
圓周
= 6π ÷ (135/360)
= 16π
圓半徑
= 16π ÷ 2π
= 8
扇形面積
= π x 8² x (135/360)
= 24π
2.
圓面積
= π x 10²
= 100π
圓心角
= (5π/100π) x 360°
= 18°
扇形的弧長
= 2 x π x 10 x (18/360)
= π
3.
設扇形半徑為 r,圓心角為 θ°。
π x r² x (θ/360) = 2 x π x r x (θ/360)
r² = 2r
r² - 2r = 0
r(r - 2) = 0
r = 0 (不合) 或 r = 2
4.
sin²30° + cos²45° + tan²60°
= (1/2)² + (1/√2)² + (√3)²
= (1/4) + (1/2) + 3
= 15/4
5.
(1)
AB² = BC² + AC² (勾股定理)
AB² = 8² + 6²
AB = 10
sinA
= BC/AB
= 8/10
= 4/5
(2)
cosA
= AC/AB
= 6/10
= 3/5
(3)
tanA
= BC/AC
= 8/6
= 4/3
6.
cosQ
= 1/secQ
= 1/√3
= √3/3
sin²Q + cos²Q = 1
sin²Q + (√3/3)² = 1
sinQ = √6/3
tanQ
= sinQ / cosQ
= (√6/3) / (√3/3)
= √2
所以 tanQ + √6 cosQ
= √2 + √6 x (√3/3)
= √2 + 3√2/3
= √2 + √2
= 2√2
7.
設 BC = 1, AC = 3
AB² = BC² + AC² (勾股定理)
AB² = 1² + 3²
AB = √10
sinA + cosA
= (BC/AB) + (AC/AB)
= (1/√10) + (3/√10)
= 4/√10
= 2(√10)/5
2013-07-17 12:08:32 補充:
發問時,點數已扣除。刪除問題只會損人不利己。