Question

比较这两个tan(-13丌/4)与tan(-17丌/5)的大小?

Answer 1

比较这两个tan(-13丌/4)与tan(-17丌/5)的大小?

tan(-13丌/4)
=tan(-4丌+3丌/4)
=tan3丌/4
=tan(丌-丌/4)
=-tan丌/4
=-1;

tan(-17丌/5)
=tan(-4丌+3丌/5)
=tan3丌/5
=tan(丌-2丌/5)
=-tan2丌/5.

丌/4=5丌/20<8丌/20=2丌/5,
∵在(0,丌/2)上,y=tanx是增函数.
∴tan(丌/4)<tan(2丌/5)
从而-tan(丌/4)>-tan(2丌/5)
即tan(-13丌/4)>tan(-17丌/5).
∴tan(-13丌/4)>tan(-17丌/5).

Answer 2

tan(-13丌/4)=tan(-13丌/4丌+4丌)=tan(3丌/4)
tan(-17丌/5)=tan(-17丌/5+4丌)=tan(3丌/5)
3丌/4>3丌/5>丌/2, tanx在[丌/2,丌]是减函数 =>
tan(3丌/4)<tan(3丌/5)
=>tan(-13丌/4)<tan(-17丌/5)