sinα=-1/3,且α是第三象限的角
所以cosa也小于0,
故cosa= -√(1-sin²a)
= -√(1-1/9)
= -2√2 /3
由公式cos(a+b)=cosa*cosb -sina*sinb可以知道,
cos(α+π/4)=cosa*cos(π/4) -sina*cos(π/4)
= (-2√2 /3) * (√2/2) - (-1/3)*(√2/2)
= -2/3 + √2 /6
而cos2a=1-2sin²a
=1- 2*(-1/3)²
=7/9