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October 4, 2015
Posted by **Don** on Tuesday, December 20, 2011 at 8:16pm.

could be

a. 5/9

b. root5/3

c. 9/4

d. 9/5

Please help.......

- Trig -
**Lindsey**, Tuesday, December 20, 2011 at 8:25pmIf sin = 2/3, the side opposite from the angle is 2 and the hypotenuse is 3, since sin is opposite over hypotenuse.

a^2 + b^2 = c^2. The hypotenuse, 3, is c, and 2 can be a. 3^2 - 2^2 is 5. Since that leaves b^2 = 5, you have to take the root of both sides, so b = root5. That means the adjacent side is root5.

Cos is adjacent over hypotenuse, so cos is root5 over 3. Sec is cos flipped, so sec is 3/root5 or 3root5/5. When you square that whole thing, you get 9 times 5 (45) divided by 25, which is the same thing as 9/5.

I hope that helped!

- Trig -
**Damon**, Tuesday, December 20, 2011 at 8:25pmsin^2 = 4/9

cos^2 = 1 - sin^2 = 5/9

1/cos^2 = sec^2 = 9/5