Question

Kąt α jest ostry, cosα=⅖. Obliczwartości pozostalych funkcji trygonometrycznych.

Answer 1

sin²α = 1 - cos²α

sin²α = 1 - (2/5)²

sin²α = 1 - 4/25

sin²α = 21/25

sinα = √21/5

 

tgα = sin/cos

tgα = √21/5 * 5/2

tgα = √21/2

 

ctgα = 1/tgα

ctgα = 2/√21

ctgα = 2√21/21

Answer 2

α ∈ (0°; 90°)

cos α = ⅖

cos²α+sin²α=1

 

sinα :cosα = tgα

tgα=√21/2

ctgα=tgα⁻¹=2√21/21