F.2 Trigonometic Ratios

2012-06-18 6:28 pm

1. Simplify ((sin30 cos60) / (tan60)) x sin60 tan45

2. If tanΘ=12/13, find the value of ((8 sinΘ)+(5 cosΘ)) / ((6 sinΘ)+(2 cosΘ))

3. Find the value of cos10 －sin80. Evaluate the value of (cos10+cos20+...........+ cos 80) －(sin 10+ sin 20+...........+ sin 80). Briefly explain how you can get the answer.

回答 (1)

用戶30507

2012-06-18 6:56 pm

✔ 最佳答案

1. ((sin30 cos60) / (tan60)) x sin60 tan45
=((1/2×1/2)/√3) x √3/2 x 1
=1/8

2. ((8 sinΘ)+(5 cosΘ)) / ((6 sinΘ)+(2 cosΘ))
=[(8 sinΘ+5 cosΘ)÷cosΘ] / [(6 sinΘ+2 cosΘ)÷cosΘ]
=(8tanΘ+5) / (6tanΘ+2)
=(8x12/13+5) / (6x12/13+2)
=161/98
=23/14

3. cos10 －sin80=sin(90-10)-sin80=sin80-sin80=0
Using cosΘ=sin(90-Θ) again, we have
(cos10+cos20+...........+cos70+ cos 80) －(sin 10+ sin 20+..........+sin70+ sin 80)
=(sin80+sin70+...+sin20+sin10)－(sin10+sin20+...+sin70+sin80)
=0

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