Question

dado x arco do primeiro quadrante, e senX: raiz de 5/5, calcule:
a) cosX
b)cosscX
c)secX
d)tgX
e)cotgX

Answer 1

a) sen² x + cos² x = 1  

(√5/5)² + cos² x = 1  

cos² x = 1 - 5/25  

cos² x = 5/5 - 1/5  

cos x = √(4/5)  

cos x = 2/√5 * √5/√5  

cos x = 2√5 /5  

b) cossec x = 1/sen x  

cossec x = 1/[(2√5)/5]  

cossec x = 1 * 5/2√5  

cossec x = 5/(2√5) * √5/√5  

cossec x = 5√5/10  

cossec x = √5/2  

c) sec x = 1/cos x  

sec x = 1/(√5/5)  

sec x = 1 * 5/√5  

sec x = 5/√5 * √5/√5  

sec x = 5√5/5  

sec x = √5  

d) tg x = sen x/cos x  

tg x = (√5/5)/(2√5/5)  

tg x = √5/5 * 5/2√5  

tg x = 5√5/10√5  

tg x = 1/2  

e) cotg x = 1/tg x  

cotg x = 1/(1/2)  

cotg x = 1 * 2/1  

cotg x = 2  

Todos positivos no 1° quadrante