What is an equation for a sine curve with amplitude 2, and period 4pi radians ? a. y=0.5sin 4 theta b. y=4sin 0/2 c. y=2sin2 0 d. y=2sin0/2 find the period and amplitude of the function. y=5 cos 2 0theta a. period: pi radians; amplitude: 2.5 b. period: pi radians: amplitude: 5 c. period: pi radians: amplitude: 2.5 d. period: pi radians; amplitude: 5 tan 2pi/3 a. sqrt3 b. 1/sqrt3 c. -sqrt3 d. 1 tan 5pi/6 a. sqrt3 b.-sqrt3/3 c.-sqrt3 d.1

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

One unique triangle, because those angles add up to 180, and that's how many degrees there are in one triangle.