Question

Trig. - Solve for x if 0 < x < 2pi, exact values only in radians.
tan ((sin^-1(4/5))/2) please show steps

Answer 1

Not sure exactly where your "x" is, but in general:
let sin^-1(4/5) = y => sin(y) = 4/5
Use sin^2 + cos^2 = 1 -> 1/tan^2(y) = [1/sin^2(y)] - 1 to find tan(y).

Use half angle forumula to find tan(y/2)

Blah. can;t be arsed to actually do it though,

Answer 2

Oppps, it is supposed to be 'Evaluate without a calculator'....Sorry

Answer 3

I don't see how that effects my method? I don't use calculators, anyway.

Answer 4

No, it doesn't, it just explains why there is no 'x'. XD

Answer 5

Thanks!!

Answer 6

No? I doesn't say what exactly you are solving for. I mean, I assume the whole expression = x, but...

Answer 7

No it doesn't effect your method is what I meant, and I am solving for tan of (sin^-1(4/5)/2), if that makes any sense. Your method seems right though.

Answer 8

My Method IS right. It's my method, after all.

Answer 9

Lol, that it is!

Answer 10

xD my method is hideously long. Sorry.

draw a RA triangle with angle y = arcsin(4/5), you can fill in the other sides {3,4,5} and find sin(y) = 4/5, cos(y) = 3/5

And tan(y/2) = sin(y) / ( 1 + cos (y) )

My bad, haven'y used half tan in a while, but the formulae are all in terms of sin and cos.

Answer 11

Lol, that works too, thanks soooo much! :)

Answer 12

You're welcome (the only problem is you may not be able to assume the formula for tan(y/2), but it's not too taxing to prove).

Answer 13

:)