Question

Kąt alfa-ostry oraz tgalfa= 4/5. Oblicz wartość wyrażenia:

3 sinα- 4cosα/2sinα

Proszę o pomoc!

Answer 1

skracamy ulamek

cosα/sinα= 1:sinα/cosα=1/tgα

(3sinα-4cosα):2sinα= 3/2-2*1/tgα=1,5-2*5/4=1,5-2,5= - 1

Answer 2

tgα=4/5

tgα=sinα/cosα

Zatem

sinα/cosα=4/5

sin²α+cos²α=1       dolaczamy 2. rownanie na jedynke trygonometryczna

 

sinα=4/5 cosα

16/25 cos²α+cos²α=1

 

41/25 cos²α=1

cos²α=25/41

cosα=5/√41

cosα=5√41/41

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sinα=(4/5)·5√41/41

sinα=4√41/41

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(3sinα-4cosα)/2sinα=(12√41/41-20√41/41)/8√41/41=(-8√41/41)·(41/8√41)=-1