Find all values of x in the interval [0, 2𝜋] that satisfy the inequality. (Enter your answer using interval notation.) 5 sin(x) > 5 cos(x)

Answer 1

5sinx>5cosx

divide by 5

sinx>cosx

pi/4<x<3pi/2

graph sinx and cosx from x=0 to 2pi

sinx=cosx when x=pi/4 or 5pi/4

cosx>sinx when 0<x<pi/4 and 5pi/4<x<2pi

x is an element of the interval (pi/4, 5pi/4) when 5sinx>5cosx

Answer 2

sinx > cosx;

sinx = cosx; tanx = 1; x = π/4 or x = 5π/4

sinx > cosx for x ∈ (π/4, 5π/4)