F3 三角比 急.要TEST

1. If Tanθ=0.5，find the values of Sinθ，Cosθand Cos^2 θ－Sin^2 θ.
Sol
Tanθ=0.5>0
=>θ在第1象限或θ在第3象限
(1) θ在第1象限
Tanθ=0.5=1/2
Sinθ=1/sqrt(5)
Cosθ=2/sqrt(5)
Cos^2 θ－Sin^2 θ=4/5－1/5=3/5
(2) θ在第3象限
Sinθ=－1/sqrt(5)
Cosθ=－2/sqrt(5)
Cos^2 θ－Sin^2 θ=4/5－1/5=3/5

Should be 3/5 intead of -4/5

tanθ=0.5=1/2

=>(sinθ)/(cosθ)=1/2

=>sinθ:cosθ=1:2

let sinθ=k and cosθ=2k ,

cos^2θ+sin^2θ=1

=>(k)^2+(2k)^2=1

=>k=1/sqrt(5)

so sinθ=1/sqrt5 and cosθ=2/sqrt5

=>sin^2θ-cos^2θ=(1/sqrt5)^2-(2/sqrt5)^2=-4/5//