Question

Wiedząć że ctg=⅔ oblicz pozostałe funkcje

Answer 1

ctgx = 2/3

 

tgx = 1/ctgx = 1 : 2/3 = 1 * 3/2 = 3/2

 

 

tgx = sinx/cosx

3/2 = sinx/cosx

2sinx = 3cosx

sinx = 3/2cosx

 

sin^2x + cos^2x = 1

(3/2 cosx)^2  cos^2x = 1

9/4 cos^x + cos^x = 1

13/4 cos^2x = 1

cos^2x = 4/13

cosx = 2√13/13     lub cosx = -2√13/13

 

sinx = 3/2 * 2√13/13     lub  sinx =  3/2 * ( - 2√13/13)

sin x = 3√√13/13           lub  sinx = -3√13/13

 

Answer 2

ctgα=2/3

tgα=1/ctgα=3/2

 

{tgα=sinα/cosα

{sin²α+cos²α=1

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{cosα=2/3 sinα

{sin²α+(2/3 sinα)²=1

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{cosα=2/3 sinα

{sin²α + 4/9 sin²α=1

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{cosα=2/3 sinα

{13/9 sin²α=1

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{cosα=2/3 sinα

{sin²α=9/13

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{cosα=2/3 sinα

{sin²α-9/13=0

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{cosα=2/3 sinα

{(sinα-3√13/13)(sinα+3√13/13)=0

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{cosα=2/3 sinα

{sinα=3√13/13  lub  sinα=3√13/13

[Odpowiedź ujemną odrzucam]

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{cosα=2/3 *3√13/13

{sinα=3√13/13

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{cosα=2√13/13

{sinα=3√13/13