Acute-angle relations: IF sin(x) = tan(y); for acute angles x and y, how are the angles related? (multiple-choice)

[Zelda22]

IF sin(x) = tan(y); for acute angles x and y,
how are the angles related?

A. congruent
B.complementary
C.supplementary
D.not enough information

I'm confused with this question; I think there is not enough information.

This is what I tried.

If sin(x)=tan(y) for acute angles x and y
sin (x)= sin(y)/cos(y)
sin(x) cos(y) = sin(y)

but I don't have the values for x and y, so I can't determine a relationship between the angles.

Please help. Is there another way to approach this question?

I know for complementary angles sin(x)=cos(y), but I don't know any relation involving sin(x) =tan (y)

 

[The Highlander]

IF sin(x) = tan(y); for acute angles x and y,
how are the angles related?

A. congruent
B.complementary
C.supplementary
D.not enough information

I'm confused with this question; I think there is not enough information.

This is what I tried.

If sin(x)=tan(y) for acute angles x and y
sin (x)= sin(y)/cos(y)
sin(x) cos(y) = sin(y)

but I don't have the values for x and y, so I can't determine a relationship between the angles.

Please help. Is there another way to approach this question?

I know for complementary angles sin(x)=cos(y), but I don't know any relation involving sin(x) =tan (y)

Have you tried plugging numbers into your calculator?

For example:-

A. Let x = y = 30° and x = y = 45° and x = y = 60°; how do sin(x) & tan(y) compare in each case? (Are they equal?)

B. Let x= 30° and y = 60° and vice versa; (you've already tried 45° and its complement at A); again compare to see if sin(x) & tan(y) are equal.

C. They can't be "supplementary" if they're both acute!

D. Do you still think there isn't enough information?

Have fun.

 

[Zelda22]

Thank you. I still think there isn't enough information. sin(x) & tan(y) are not equal.

 

[blamocur]

Thank you. I still think there isn't enough information. sin(x) & tan(y) are not equal.

I find this multiple-choice problem rather poorly stated. IMHO, none of the choices is correct. I see enough information to say that [imath]y=\arctan(\sin (x))[/imath], but whoever created the question most likely thought that D is the correct answer.

 

[The Highlander]

Thank you. I still think there isn't enough information. sin(x) & tan(y) are not equal.

I would agree with @blamocur (that none of the choices are correct) and that the author probably expected D to be given as the best choice.
If you did the little 'experimentation' I suggested then should then have been in possession of enough information to know that A, B & C were all not valid answers which leads me to the conclusion that D is not a 'correct' answer either but it's what you might (at a pinch) consider less wrong than the others.

 

[Zelda22]

Why is D incorrect too?

 

[blamocur]

Why is D incorrect too?

Looks to me more like a language -- where I am pretty ignorant -- problem rather than math. D is "correct" in the sense that none of A,B,C can be confirmed or denied. I would pick D on an exam myself because, as I stated earlier, whoever created the question most likely thought that D is the correct answer.