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

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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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