calculus

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1. what trig function has an amplitue of 1 and negative values for angles between π/2 and π?

2. what trig function never crosses the x-axis and has a value of 2 at π/6?

are these correct?
3. what trig function has a period of π and is undefined for -π/2, π/2, 3π/2...
answer: y=tan x?

4. what trig function has a period of 2π, is continuous, and is increasing for 0 < x < π/2?
answer: y=sin x?

  • calculus -

    1. An amplitude of 1 applies to only the sine or cosine function.
    the given domain puts the angle in the 2nd quadrant.
    in that quad, the sine is positive and the cosine is negative, so it has to be
    y = cosx

    2. I know that sin30° = sin(π/6) = 1/2
    so csc (π/6) = 2
    and we know that the cosecant has values ≥1 or ≤-1 , never crossing the x-axis
    so y = cscx

    3. you are correct
    4. you are correct

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