Value of y

1. Nov 30, 2009

xpack

http://img194.imageshack.us/img194/1383/68225760.png [Broken][/URL]

sin-1x=y & siny=x
tan-1x=y & tany=x

The answer is E but I dont know how my teacher got to that. Can someone explain this to me please?
1. The problem statement, all variables and given/known data

Last edited by a moderator: May 4, 2017
2. Nov 30, 2009

n!kofeyn

Do you understand the inverse trig functions? The inverse trig functions find the angle of the triangle that satisfies the given relation. That is sin-1(t) is the angle theta such that sin(theta)=t. If you view t as t/1, then can you set up a triangle that has this property? Can you then find the length of the remaining edges so that you can find tan(theta), i.e. tan(sin-1(t))?

3. Nov 30, 2009

xpack

I'm still very confused

4. Nov 30, 2009

n!kofeyn

Okay. Set θ=sin-1(t). This means that sin(θ)=t (i.e. sin(θ)=t/1). This means that in a right triangle with one angle that is θ, the side opposite θ has length t and the hypotenuse has length 1. You can find the side adjacent to θ by using the Pythagorean theorem. Then all you have to do is find tan(θ) since tan(θ)=tan(sin-1(t)).

5. Nov 30, 2009

xpack

Okay, thank you so much you cleared that right up!

6. Nov 30, 2009

n!kofeyn

No problem! That is the general technique when doing these type of trig problems that contain inverse trig functions.