Question

What is an equation for a sine curve with amplitude 2, and period 4pi radians ?

Answer 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)
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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

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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

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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