Question

Kat alfa jest ostry i cos alfa =5/7. obilcz tg i ctg alfa.

Answer 1

α∈(0°;90°)

cosα=⁵/₇

 

cos²α+sin²α=1

(⁵/₇)²+sin²α=1

²⁵/₄₉+sin²α=1

sin²α=²⁴/₄₉

sinα=²/₇√6

 

tgα=sinα/cosα

tgα=²/₇√6 / ⁵/₇=²/₅√6=0,4√6

 

ctgα=1/tgα

ctgα=1/0,4√6=2,5√6/6=5√6/12

Answer 2

 

cosα = 5/7

 

sin²α + cos²α = 1

(5/7)² + sin²α = 1

25/49 + sin²α = 1

sin²α = 24/49

sinα = √24/7 ∨ sinα = -√24/9 <-- kąt jest ostry, więc to odpada

 

tgα = sinα/cos

 

tgα = √24/7 / 5/7 = √24/5 = 2√6/5

 

ctgα = 1/tgα

 

ctg = 1/2√6/5 = 5/2√6 = 5√6/12

 

 

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