Question

Considere que Senß= 3/5.
Determine o valor exato de:
a) Cos^2ß
b) tanß
(20 pontos!!!)

Answer 1

Vamos lá: Usando a relação fundamental da trigonometria teremos:

Resolvendo a a):

$sen^2\beta+cos^2\beta=1\implies cos^2\beta=1-sen^2\beta\\sen\beta=\dfrac{3}{5}\implies sen^2\beta=\dfrac{9}{25}\\cos^2\beta=1-sen^2\beta\implies cos^2\beta=1-\dfrac{9}{25}\implies cos^2\beta=\dfrac{16}{25}=0,64$

Disso temos que $\cos^2\beta=0,64$. Agora para resolver a b) primeiro determinaremos o valor de cos b e depois usaremos a definição de tangente:

$\sqrt{cos^2\beta}=\sqrt{\dfrac{16}{25}}\implies cos\beta=\dfrac{4}{5}\\tan\beta=\dfrac{sen\beta}{cos\beta}\implies tan\beta=\dfrac{\frac{3}{5}}{\frac{4}{5}}\implies tan\beta=\dfrac{3}{5}\cdot\dfrac{5}{4}=\dfrac{3}{4}=0,75$

Logo a $tan\beta=0,75$