Would someone verify these answers.
1. A person waves his hand back and forth, where their finger tips move past the starting position 4 cm in each direction. If he waves 20 times every 15s, what sine equation models the movement of the hand if the hand starts in the upright position and the right direction will be taken as positive?
a)y=4sin(20pi/15 x t)
b)y=4sin(30pi/20 x t)
c)y=4sin(40pi/15 x t)
c)y=8sin(30pi/20 x t)
Answer: A
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2. Which of the six trig functions are positive in quad III?
Ans: Tangent and cotangent
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3. What is the exact value of sin(3pi/2)?
Answer: 3pi/2=270 degree, equals to -1
Therefor exact value -1.
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1.
If he waved once every second, the frequency would be 1. you'd have sin(2πt).
If he waved n times, you'd have sin(2πnt).
Would you like to change your answer to C?
2. ok
3. ok
Hmm. If a wave is defined as moving away from the starting point and back, your A answer is correct.
If a wave is defined as a complete cycle away and back in each direction, then the answer would be C.
I am confused for number 3
sin(270) = sin(90+180) = sin90cos180 + cos90sin180 = 1(-1) + 0*0 = -1
or, at 270 deg, y=-1, x=0, r=1
sin = y/r = -1/1 = -1
1. Well, isn't this person just waving hello to a whole new level? So their hand goes back and forth, covering a distance of 4 cm in each direction. And they do this waving extravaganza 20 times every 15 seconds. To model this masterpiece using a sine equation, we need to consider the hand's starting position and the direction of positive movement. Given that the hand starts upright and the right direction is the positive direction, we can go with option A, which is y = 4sin(20π/15 x t). It's the perfect equation to capture the magic of this hand-waving wonder.
2. Ah, quad III, the quadrant that would make a great spot for a villain lair in a superhero movie. So which trig functions embrace the darkness in this quadrant? Well, it's the tangent and cotangent functions that shine in quad III. They positively thrive in that villainous corner of the coordinate plane. Watch out, heroes!
3. Ah, the exact value of sin(3π/2). So we're heading into the realm of the unit circle here. When we look at 3π/2 on the unit circle, we find ourselves at the lovely angle of 270 degrees. And at that point, the sine function takes a dip and reaches the exact value of -1. So in this case, our exact value for sin(3π/2) is -1.
To verify the answers given:
1. The equation that models the movement of the hand is y = 4sin(20pi/15 * t). In this equation, "y" represents the position of the hand, "t" represents time, and 20pi/15 is the frequency of the hand waves. The amplitude of the hand movement is 4 cm in each direction, as stated in the question. Therefore, the correct answer is a) y = 4sin(20pi/15 * t).
2. In quadrant III, the x-coordinate is negative and the y-coordinate is negative. The trigonometric functions that are positive in quadrant III are tangent (tan) and cotangent (cot). Therefore, the answer is tangent and cotangent.
3. To find the exact value of sin(3pi/2), we need to look at the unit circle. In the unit circle, 3pi/2 represents an angle of 270 degrees or -90 degrees. At this angle, the y-coordinate is -1. Therefore, the exact value of sin(3pi/2) is -1.
Based on the explanations given, the answers provided are correct.