標題:
發問:
解方程 1.sinθ+cosθ=0 2.2cos^2θ+cosθ=0 3.5sin^2θ-2sinθcosθ-3cos^2θ=0 4.cos(3θ-45°)=1/2 一定要有步驟 唔該各位
最佳解答:
設所求θ之範圍為： 0 ≤ θ ≤ 360° ===== 1. sinθ + cosθ = 0 sinθ = -cosθ sinθ/cosθ = -1 tanθ = -1 θ = (180-45)°, (360-45)° θ = 135°, 315° ===== 2. 2cos2θ + cosθ = 0 cosθ(2cosθ + 1) = 0 cosθ = 0 或 cosθ = -1/2 θ = 90°, 270° 或 θ = (180-60)°,(180+60)° θ = 90°, 120°, 240°, 270° ===== 3. 5sin2θ - 2sinθcosθ - 3cos2θ = 0 (5sin2θ - 2sinθcosθ - 3cos2θ) / cos2θ = 0 5tan2θ - 2tan - 3 = 0 (5tanθ + 3)(tanθ - 1) = 0 tanθ = -3/5 或 tanθ = 1 θ = (180-30.96)°, (360-30.96)° 或θ = 45°, (180+45)° θ = 45°, 149.04°, 225°, 329.04° ===== 4. 0 ≤ θ ≤ 360° 0 ≤ 3θ ≤ 1080° -45° ≤ (3θ-45°) ≤ 1035° cos(3θ-45°) = 1/2 3θ-45° = 60°, (360-60)°, (360+60)°, (720-60)°, (720+60)°, (1080-60)° θ = 35°, 115°, 155°, 235°, 275°, 355°
其他解答:
.sinθ+cosθ=0 sinθ=-cosθ tanθ=-1 θ=225° --------------------- 2cos^2θ+cosθ=0 cosθ(2cosθ+1)=0 cosθ=0 or -1/2 θ=90° 120° 240° or 270° --------------------- 5sin^2θ-2sinθcosθ-3cos^2θ=0 5tan^2 θ - 2tanθ - 3 = 0 [Whole line / cos^2 θ] (tanθ-1)(5tanθ+3)=0 tanθ=1 or -3/5 θ=45° 149° 225° or 329° ---------------------- cos(3θ-45°)=1/2 3θ-45° = 60° or 300° θ=35° or 115°4E350C6F8B48ECA2
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三角函數幾條問題發問:
解方程 1.sinθ+cosθ=0 2.2cos^2θ+cosθ=0 3.5sin^2θ-2sinθcosθ-3cos^2θ=0 4.cos(3θ-45°)=1/2 一定要有步驟 唔該各位
最佳解答:
設所求θ之範圍為： 0 ≤ θ ≤ 360° ===== 1. sinθ + cosθ = 0 sinθ = -cosθ sinθ/cosθ = -1 tanθ = -1 θ = (180-45)°, (360-45)° θ = 135°, 315° ===== 2. 2cos2θ + cosθ = 0 cosθ(2cosθ + 1) = 0 cosθ = 0 或 cosθ = -1/2 θ = 90°, 270° 或 θ = (180-60)°,(180+60)° θ = 90°, 120°, 240°, 270° ===== 3. 5sin2θ - 2sinθcosθ - 3cos2θ = 0 (5sin2θ - 2sinθcosθ - 3cos2θ) / cos2θ = 0 5tan2θ - 2tan - 3 = 0 (5tanθ + 3)(tanθ - 1) = 0 tanθ = -3/5 或 tanθ = 1 θ = (180-30.96)°, (360-30.96)° 或θ = 45°, (180+45)° θ = 45°, 149.04°, 225°, 329.04° ===== 4. 0 ≤ θ ≤ 360° 0 ≤ 3θ ≤ 1080° -45° ≤ (3θ-45°) ≤ 1035° cos(3θ-45°) = 1/2 3θ-45° = 60°, (360-60)°, (360+60)°, (720-60)°, (720+60)°, (1080-60)° θ = 35°, 115°, 155°, 235°, 275°, 355°
其他解答:
.sinθ+cosθ=0 sinθ=-cosθ tanθ=-1 θ=225° --------------------- 2cos^2θ+cosθ=0 cosθ(2cosθ+1)=0 cosθ=0 or -1/2 θ=90° 120° 240° or 270° --------------------- 5sin^2θ-2sinθcosθ-3cos^2θ=0 5tan^2 θ - 2tanθ - 3 = 0 [Whole line / cos^2 θ] (tanθ-1)(5tanθ+3)=0 tanθ=1 or -3/5 θ=45° 149° 225° or 329° ---------------------- cos(3θ-45°)=1/2 3θ-45° = 60° or 300° θ=35° or 115°4E350C6F8B48ECA2
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