Question

Oblicz pozostalem wartosci funkcji trygonometrycznych wiedzac że:

α ∈ (0*,90*)

Ctgα=3

// Skorzystaj ze wzorów!

Sin²α+cos²α=1

tga= sina/cosa

ctaa= 1/tga

tga= 1/ctga

Answer 1

ctga = 3

 

tga = 1/ctga

tga = 1/3

 

tga = sina / cosa

1/3 = sina/cosa

cosa = 3sina

 

sin²a + cos²a = 1

sin²a + (3sina)² = 1

sin²a + 9sin²a = 1

10sin²a = 1

sin²a = 1/10

sina = √10 / 10

 

cosa = 3 * √10 / 10

cosa = 3√10 / 10

Answer 2

ctgα=1/tgα

3=1/tgα

tgα=⅓

ctgα=cosα/sinα

sinα=√[1-cos²α]

 

3=cosα/ √[1-sin²α]   /²

9=cos²α/[1-cos²α]

 

9-9cos²α=cos²α

9=9cos²α+cos²α

10cos²α=9

cos²α=9/10

cosα=3/√10=3√10/10

...........................................

 

sinα=√[1-cos²α]=√[1-9/10]=√1/10=√10/10