Show that cos(sin^(-1) v + cos^(-1) v) = 0.

Results 1 to 7 of 7

- November 12th 2008, 07:18 AM #1

- Joined
- Jul 2008
- From
- NYC
- Posts
- 1,489

- November 12th 2008, 07:31 AM #2
Let and

First, we can rewrite using the identity

Its good to note that and [why do you think this is the case?]. So our expression can be written as

-------------------------------------------------------------------------

Now let's construct two different triangles, one that has an angle and an angle

Starting with , we see that the side opposite of the angle has a value of and that the hypotenuse has a value of . Using the pythagorean theorem, we can find the value of the adjacent side:

-------------------------------------------------------------------------

Now, we construct at triangle for . We see that the side adjacent of the angle has a value of and that the hypotenuse has a value of . Using the pythagorean theorem, we can find the value of the opposite side:

-------------------------------------------------------------------------

Now what do you think equals?

--Chris

- November 12th 2008, 07:35 AM #3

- Joined
- Apr 2005
- Posts
- 15,714
- Thanks
- 1472

- November 12th 2008, 07:44 AM #4

- November 12th 2008, 04:40 PM #5

- Joined
- Jul 2008
- From
- NYC
- Posts
- 1,489

- November 12th 2008, 04:41 PM #6

- Joined
- Jul 2008
- From
- NYC
- Posts
- 1,489

- November 12th 2008, 06:30 PM #7