Math.. help!!

2010-07-29 1:44 am

1) tan θ=12/13, find the value of 8 sinθ +5 cosθ / 6 sinθ +2 cosθ.

2) find the value of cos 10° - sin 80°. Evaluate the value of (cos 10°+cos 20°+......+cos 80°)-(sin 10°+sin 20°+......+sin 80°). Briefly explain how you can get the answer.

回答 (1)

用戶2053

2010-07-29 2:21 am

✔ 最佳答案

1)
(8 sinθ + 5 cosθ) / (6 sinθ +2 cosθ)= [ (8 sinθ + 5 cosθ) / cos θ ] / [ (6 sinθ + 2 cosθ) / cos θ]= (8 tanθ + 5) / (6 tanθ + 2)= [8(12/13) + 5] / [6(12/13) + 2]= (161/13) / (98/13)= 161/98= 23/142)
cos 10° - sin 80°= sin(90° - 10°) - sin80°= 0Form 8 groups such that each group are equal to 0 :(cos 10°+cos 20°+......+cos 80°) - (sin 10°+sin 20°+......+sin 80°)= (cos 10° - sin 80°) + (cos 20° - sin70°) + (cos 30° - sin60°) + ...
+ (cos 80° - sin 10°)= (sin80° - sin 80°) + (sin 70° - sin70°) + (sin 60° - sin60°) + ...
+ (sin 10° - sin 10°)= 0 + 0 + 0 + ... + 0= 0

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