IDENTIFY THE CRITICAL POINTS IN THE PRINCIPAL CYCLE Y= TAN(1/2Ꝋ+30⁰)

Question

need answers for

left side

right side

Period

Quarter point

midpoint

three quarter point

Answer 1

y = tan[(1/2)θ + 30°]

-90° < (1/2)θ + 30° < 90°

-120° < (1/2)θ < 60°

-240° < θ < 120°

Period = 120° - (-240°) = 360°

Left endpoint = -240°

Right endpoint = 120°

Midpoint = -240° + 360°/2 = -60°

Quarter Point = -240° + 360°/4 = -150°

Three Quarter Point = -240° + (3/4)(360°) = 30°