Question

设三角形的内角ABC对边分别为abc,函数f（B）=2分之根号3sinB+sin2分之B平方+1

Answer 1

(1)

f(B) = √3/2 sinB + sin²B/2 + 1

= √3/2 sinB - 1/2 cosB + 3/2

= sin(B - π/6) + 3/2

f(B) ∈ (1 ,5/2]

(2)

f(B) = 3/2

B = π/6

a/sinA = b/sinB = c/sinC

C = π/3 ,A = π/2 ,a = 4

或 C = 2π/3 ,A = π/6 ,a = 2