Question

已知a∈(π/2,π),sina=3/5,求tan(a+π/4)

Answer 1

a第二象限
所以cosa<0
sin²a+cos²a=1
所以cosa=-4/5
tana=sina/cosa=-3/4

tanπ/4=1
所以原式=(tana+tanπ/4)/(1-tanatanπ/4)
=1/7

Answer 2

tan(α+π/4）=（tan(α)+tan(π/4))/(1-tanα*tan(π/4))=(1+tanα)/(1-tanα)
sina=3/5 cosa= - 4/5
tana= - 3/4
原式等于1/7

Answer 3

解：因为sinα=3/5，所以cosα=4/5，tanα=3/4
因为tan（α+π/4）=（tanα+1）/（1-tanα）=7

Answer 4

首先算出tana=-3/4(因为a在第二象限，所以tana为负）然后用公式tan(a+π/4)=tana+tanπ/4/1-tana*tanπ/4=-3/4+1/1-(-3/4)*1=1/7