Question

se senx = 2/3 , com π/2 < x < π, determine cosx, tgx, cossecx e secx.​

Answer 1

sex2 + cosx2 = 1

( 2/3 ) 2 + cosx2 = 1

4 / 9 + cosx2 = 1

cosx,2 = 1 - 4 / 9

cosx2 = 9 / 9 - 4 / 9

cosx2 = 5 / 9

cosx = √5/9

cosx = √5 / 3 ( valor vai ser negativo)

cosx = - √5 / 3

tagx = 2 / 3 ÷ ( - √5 ) / 3

tagx = 2 / 3 • ( 3 ) / - √5

tagx = - 2 / √5 ( racionalizar )

tag x = -2√5 / 5

cossecx = 1 ÷ 2 / 3

cossecx = - 2 / 3

secx = 1÷ ( - √5 / 3)

sec x = 3/ √5

secx = 3√5 / 5