Trigonometry Help: Evaluating sin2y & cos2y

[huntingrdr]

Homework Statement

If sin x = 1/3 and sec y = 5/4, where x and y lie between 0 and pi/2, evaluate the expression.

sin2y

cos2y

Homework Equations

2siny = 2siny*cosy?

cos2y = cos^2 y - sin^2 y?

The Attempt at a Solution

I think sin2y goes to 2siny*cosy. I know what sin x is but how do I find sin y? The answer should be 24/25 for siny, but not sure how to get it. Not sure what the answer is or how to get it for cos2y.

 

[Mark44]

First thing you should do is to draw two right triangles, one with an angle x and the other with an angle y. In the first triangle, you have that sin x = 1/3, so make the side opposite angle x 1 unit, and make the hypotenuse 3 units. You should be able to figure out the length of the side adjacent to angle x, so you can determine cos x.

For the other triangle, you're given that sec y = 5/4, so cos y = 4/5 (sec y = 1/(cos y)). In that triangle, label the hypotenuse 5 units and the adjacent side 4 units. What does the side opposite y need to be? Once you find it, you can find sin y.