<span>1. a sine curve with amplitude 2, and period 4pi radians </span> the general equation of the sine curve ⇒⇒ y = a sin (nθ) where: a is the amplitude and n = 2π/perid ∵ <span>amplitude 2, and period 4pi radians </span> ∴ y = 2 sin (θ/2)
The correct answer is option D. y = 2 sin (θ/2) ===========================================
<span>2.The period and amplitude of the function ⇒⇒ y = 5 cos 2θ </span> <span>comparing with y = a cos nθ </span> where : a is the amplitude and n = 2π/period <span>amplitude = 5 , period = 2π/n = 2π/2 = π </span>
The correct answer is option B. Period: pi radians: Amplitude:5
============================================================ 3. tan (2π/3) = tan 120° = -√3 120° lie in the second quadrant and its reference angle = 180° - 120° = 60° tan function in the second quadrant is negative ∴ tan 120° = - tan 60 = -√3
The correct answer is C. -sqrt3
===================================================== 4. <span>Tan 5π/6 = tan 150° = -(√3)/3 </span> 150° lies in the second quadrant and its reference angle = 180° - 150° = 30° tan function in the second quadrant is negative ∴ tan 150° = - tan 30 = -(√3)/3
