Question

Considerando tg58=8/5 determine o valor de:
a) cos32 b) sen32

Answer 1

boa tarde

tg(58) = sen(58)/cos(58) = 8/5

5sen(58) = 8cos(58)

sen(58) = 8cos(58)/5

sen²(58) + cos²(58) = 1

64cos²(58)/25 + cos²(58) = 1

64cos²(58)/25 + 25cos²(58)/25 = 25/25

89cos²(58) = 25

cos²(58) = 25/89

cos(58) = 5√89/89

sen(58) = 8cos(58)/5

sen(58) = 8√89/89

agora

a) cos(32) = sen(58) = 8√89/89 = 0.848

b) sen(32) = cos(58) = 5√89/89 = 0.529