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Q1. What is the value of sin(π/6)?
Solution:
The value of sin(π/6) is 1/2.
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Q2. What is the x-intercept of the function y = cos(x) in the interval [0, 2π]?
Solution:
The cosine function equals zero at x = π/2 and x = 3π/2. The x-intercepts in [0, 2π] are π/2 and 3π/2.
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Q3. What is the vertical shift of the function y = tan(x) + 2?
Solution:
The vertical shift is determined by the constant added to the function, which is +2.
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Q4. 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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Q5. 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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Q6. 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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Q7. What is the vertical asymptote of y = tan(x)?
Solution:
The vertical asymptotes of the tangent function occur at x = π/2 + nπ, where n is an integer.
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Q8. Which of the following is the correct phase shift of y = sin(x - π/4)?
Solution:
The phase shift is found by setting the inside of the sine function to zero, giving a shift of π/4 to the right.
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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. What is the frequency of the function y = sin(2x)?
Solution:
The frequency of y = sin(Bx) is |B|/(2π). Here, B = 2, so the frequency is 2/(2π) = 1/π.
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