標題:
maths...20pts!
發問:
The angle α is in the 3rd quadrant and satisfies cos^2 α = 9/25, β is in 2nd qurdrant and satisfies sinβ = 12/13, while γ is in the 4th quadrant and satisfies tanγ = 7/24. Find the precise value of each of the following quantities, explaining every step of... 顯示更多 The angle α is in the 3rd quadrant and satisfies cos^2 α = 9/25, β is in 2nd qurdrant and satisfies sinβ = 12/13, while γ is in the 4th quadrant and satisfies tanγ = 7/24. Find the precise value of each of the following quantities, explaining every step of ur argument. a) cos(α+β) b) sin(α+γ) c) tan(α-β) d) sin(β+γ)
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最佳解答:
First quadrant sin & cos +ve Second quadrant sin +ve, cos -ve Third quadrant sin & cos - ve Fourth quadrant sin -ve, cos +ve Third quadrant : cos^2α = 9/25 cosα = -3/5, sinα = -4/5, tanα = 4/3 Second quadrant sinβ = 12/13 cosβ = -5/13, tanβ = -12/5 Fourth quadrant : tanγ = -7/24 (cannot be positive) sinγ = -7/25, cosγ = 24/25 (a) cos(α + β) = cosα cosβ - sinα sinβ = (-3/5)(-5/13) - (-4/5)(12/13) = 3/13 + 48/65 = 63/65 (b) sin(α + γ) = sinα cosγ + sinγ cosα = (-4/5)(24/25) + (-7/25)(-3/5) = -96/125 + 21/125 = -75/125 = -3/5 (c) tan(α - β) = (tanα - tanβ) / (1 + tanα tanβ) = [(4/3) - (-12/5)] / [1 + (4/3)(-12/5)] = [(20 + 36)/15] / [1 - 48/15] = -56/33 (d) sin(β + γ) = sinβ cosγ + sinγ cosβ = (12/13)(24/25) + (-7/25)(-5/13) = 288/325 + 35/325 = 323/325
其他解答:A9A3995907B431A4
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