How do you find the amplitude, period and phase shift for #y=1/4tan2(theta+30^circ)+3#?

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Answer 1 · 2018-03-18T11:30:18

#"Amplitude " = "None"#, Function tan x does not have amplitude.

# "Period" = P = pi / |B| = pi / 2#

#"Phase Shift " = (-C) / B = -60^@ / 2 = -pi / (3 * 2) = -pi / 6#

# "Vertical Shift " = D = 3#

Standard Form #y = A tan (Bx - C) + D#

Given : #y = (1/4) tan (2(theta + 30^@) + 3#

#"Amplitude " = "None"#, Function tan x does not have amplitude.

# "Period" = P = pi / |B| = pi / 2#

#"Phase Shift " = (-C) / B = -60^@ / 2 = -pi / (3 * 2) = -pi / 6#

# "Vertical Shift " = D = 3#

graph{(1/4) tan (2x + (pi/3)) + 3 [-10, 10, -5, 5]}