1. a sine curve with amplitude 2, and period 4pi radians
the general equation of the sine curve ⇒⇒ y = a sin (nθ)
where: a is the amplitude and n = 2π/perid
∵ amplitude 2, and period 4pi radians
∴ y = 2 sin (θ/2)
The correct answer is option D. y = 2 sin (θ/2)
===========================================
2.The period and amplitude of the function ⇒⇒ y = 5 cos 2θ
comparing with y = a cos nθ
where : a is the amplitude and n = 2π/period
amplitude = 5 , period = 2π/n = 2π/2 = π
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. Tan 5π/6 = tan 150° = -(√3)/3
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
The correct answer is B.-sqrt3/3