Math Need Help Please FAST TEST TRIG

Question

Solve cos(π/2+x)+sin(π/2+x) = 0 for [0,2π). Please show you work.

Answer 1

cos(π/2 + x) = -sin(x)

sin(π/2 + x) = cos(x)

Your problem becomes -sin(x) = cos(x) for x ∈ [0, 2π). We know that sin(x) = cos(x) at x = π/4, but the negative sign tells us that we should be looking for a solution in a quadrant that sin and cos are of opposite signs (Q2 or Q4). Thus,

x = 3π/4

x = 7π/4