Algebra 2

Find the values of the inverse function in radians.

sin^-1(0.65)

a. 0.71+2pi n and -0.71+2pi n
b. 0.71+2pi n and -3.85+2pi n
c. 0.86+2pi n and -0.86 +2pi n
d. -0.61+2pi n and 2.54+2pi n

2. tan^-1(0.09)

a.-0.09+2pi n
b. no such angle exists
c.-1.48+ pi n
d. -0.09+ pi n

I've been stuck on these two for such a long time. I think the first one is a. I don't know about the second one. I feel like it's b, if not, then either a or d... I can't seem to figure it out anymore

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asked by Fading
  1. Nevermind, the answers were b and d:/

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    posted by Fading
  2. #1
    the solutions from 0 to 2π
    would be .71 and π - .71
    or .71 and 2.43

    so I was expecting to see:
    .71 + 2π , 2.43 + 2π

    I don't see that, but when n = 0 , the first part of the solution should work
    e.g. sin(-.71) ≠ .65 , so not A
    sin *.86) ≠ .65, not C
    sin (-.61) ≠ .65, not D
    that leaves B.
    notice when n = -1
    2.43-2π = -3.85 <--- a 2nd quadrant angle

    the correct choice is B

    What a poor way to state the answer!!

    #2
    tan^-1 (.09) = .089 or π + .089
    = .089 or 3.23
    So my solution would be
    .089 + π, 3.23 + π
    again, this is not shown, so are they being sneaky again??
    clearly B is wrong, since I found answers
    tan(-.09) = -.09 , so NOT A
    tan(-1.48) = -10.98 , so NOT C

    bogus question!

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    posted by Reiny
  3. If D is the choice , then when n = 0, we get
    tan(-.09) = -.09 which is NOT the given

    D is wrong

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    posted by Reiny
  4. 2. tan^-1(-0.09)
    the answer would be D believe it or not -0.09+ pi(n)
    the first question is correct however the answer would be B
    0.71+2 pi (n) and -3.85+ 2 pi (n)
    apologies for the confusing writing I don’t have the pi symbol on hand.
    (the answers are verified and correct)

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    posted by Shane

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