Question

一、解答题。(解答题应写出必要的文字说明、证明过程及演算步骤。)

Answer 1

(1)
sin(α - π/2) = -sin(π/2 - α) = -cosα
cos(3π/2 - α) = cos[2π - (π/2 + α)] = cos[-(π/2 + α)] = cos(π/2 + α) = -sinα
tan(π/2 - α) = sin(π/2 - α)/cos(π/2 - α) = cosα/sinα
tan(-α - π) = -tan(α + π) = -tanα = -sinα/cosα
sin(-α - π) = -sin(α + π) = -sinα
原式 = -cosα(-sinα)(cosα/sinα)/[(-sinα/cosα)(-sinα)]
= cos³α/sin²α

(2)
P(-4, 3)
cosα = -4/√[(-4)² + 3²] = -4/5
sinα = 3/5
f(α) = (-4/5)³/(3/5)² = -64/45