Question

20. Resolva as seguintes equações em R. a) 2 sen x - 1 = cossec x b) 2. sen²x - 3 sen x + 1 = 0​

Answer 1

Vamos lá.

a)

2sen(x) - 1 = cossec(x)

1/sen(x) = 2sen(x) - 1

1 = 2sen²(x) - sen(x)

2sen²(x) - sen(x) - 1 = 0

y = sen(x)

2y² - y - 1 = 0

delta

d² = 1 + 8 = 9

d = 3

y1 = (1 + 3)/4 = 1

y2 = (1 - 3)/4 = -1/2

sen(x) = 1 , x = π/2, x = 5π/2

sen(x) = -1/2 , x = -π/6, x = 7π/6

b)

2sen²(x) - 3sen(x) + 1 = 0

y = sen(x)

2y² - 3y + 1 = 0

delta

d² = 9 - 8 = 1

d = 1

y1 = (3 + 1)/4 = 1

y2 = (3 - 1)/4 = 1/2

sen(x) = 1, x =  π/2, x = 5π/2

sen(x) = 1/2 , x =  π/6, x = 5π/6