Question

Sinx=2/3,xE(9,90grade), cosx=?,tgx=?,ctgx=?

Answer 1

Răspuns:

Explicație pas cu pas:

sin x = 2/3   ; x ∈ (0° ; 90°)

----------------------------------

sin²x = (2/3)² = 4/9

cos²x = 1-sin²x = ⁹⁾1-4/9 = 5/9 =>

cos x = √(5/9) = √5 /3

-------------------------------------

tg x = sin x / cos x = 2/3 : √5/3  = 2/3 · 3/√5 = 2/√5 = 2√5/5

ctg x = cos x / sin x = √5/3 : 2/3 = √5/3 ·3/2 = √5/2

Answer 2

$\it x\in(0,\ 90^o),\ sinx=\dfrac{2}{3}\\ \\ \\ cosx=\sqrt{1-sin^2}=\sqrt{1-\Big(\dfrac{2}{3}\Big)^2}=\sqrt{1-\dfrac{4}{9}}=\sqrt{\dfrac{5}{9}}=\dfrac{\sqrt5}{3}$

$\it tgx=\dfrac{sinx}{cosx}=\dfrac{\dfrac{2}{3}}{\dfrac{\sqrt5}{3}}=\dfrac{2}{\not3}\cdot\dfrac{\not3}{\sqrt5}=\dfrac{^{\sqrt5)}2}{\ \ \sqrt5}=\dfrac{2\sqrt5}{5}\\ \\ \\ tgx=\dfrac{2}{\sqrt5},\ \ ctgx=\dfrac{1}{tgx}=\dfrac{\sqrt5}{2}$