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Q1. For the function y = sin(3x), what is the period?
Solution:
The period is calculated as 2π divided by the coefficient of x, which is 3, giving a period of 2π/3.
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Q2. What is the range of the function y = 2sin(x)?
Solution:
The range of y = 2sin(x) is [-2, 2] because the sine function oscillates between -1 and 1.
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Q3. What is the period of the function y = sin(x)?
Solution:
The period of the sine function is 2π.
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Q4. At what value of x does the function y = tan(x) have a vertical asymptote?
Solution:
The tangent function has vertical asymptotes at x = π/2 + nπ, where n is an integer. The first asymptote in [0, π] is at π/2.
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Q5. What is the amplitude of the function y = 3cos(2x)?
Solution:
The amplitude is the coefficient in front of the cosine function, which is 3.
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Q6. What is the range of the function y = 4sin(x)?
Solution:
The range of y = Asin(Bx) is [-|A|, |A|]. Here, A = 4, so the range is [-4, 4].
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Q7. What is the phase shift of y = 4sin(2x + π)?
Solution:
The phase shift is found by setting 2x + π = 0, leading to a shift of -π/2.
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Q8. What is the value of sin(π/6)?
Solution:
The value of sin(π/6) is 1/2.
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Q9. What is the maximum value of y = -2cos(x)?
Solution:
The maximum value occurs when cos(x) = -1, giving a maximum of -2 * -1 = 2.
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Q10. Which of the following is the amplitude of the function y = 3sin(x)?
Solution:
The amplitude of a sine function y = Asin(Bx) is |A|. Here, A = 3, so the amplitude is 3.
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