if 0 smaller and equal θ smaller and equal 2 pi, find tan(-5pi/3)

Question

if 0 smaller and equal θ smaller and equal 2 pi, find tan(-5pi/3)

show works please

Answer 1

Mary, here's how I would tackle this.

tan(-5π/3) = tan(-5π/3 + 2π) . . . . . since the value of tan repeats every kπ radians, for k = 0, ±1, ±2, . . .

= tan(π/3)

= √3

Answer 2

tan (-5pi/3) is the same as tan pi/3

If you go in the - 5pi/3 direction you make nearly one

full rotation clockwise. A full rotation would be 2pi

or 6pi/3 so -5pi/3 is pi/3 short of this

tan pi/3 =sqroot 3