Question

2: dado senx 3/5, com x < 90° ≤ 180°, calcule

a)cosx
b)tgx
c)cotgx
d)sencx
e)cossecx

Answer 1

A) sen$^{2}$x + cos$^{2}$x = 1

$(\frac{3}{5})^{2}$ + cos$^{2}$x = 1

cos$^{2}$x = 1 - $(\frac{3}{5})^{2}$

cos$^{2}$x = 1 - $\frac{9}{25}$

cos$^{2}$x = $\frac{16}{25}$

cos x = $\frac{+}{-} \sqrt{\frac{16}{25} }$

cos x = $\frac{+}{-}$ $\frac{4}{5}$

90° < x < 180°

cos x = - \frac{4}{5}[/tex]

B)

tg x = $\frac{sen x}{cos x}$

tg x = $\frac{\frac{3}{5} }{-\frac{4}{5} }$

tg x = $-\frac{3}{4}$

C)

cotg x = $\frac{1}{tg x}$

cotg x = $\frac{1}{-\frac{3}{4}}$

cotg x = 1 . $-\frac{4}{3}$

cotg x = -\frac{4}{3}[/tex]

D)

sec = \frac{1}{cos x}[/tex]

sec = $\frac{1}{-\frac{4}{5}}$

sec = $-\frac{5}{4}$

D)

cossec = $\frac{1}{sen x}$

cossec = $\frac{1}{\frac{3}{5} }$

cossec = $\frac{5}{3}$