# Drawing a right triangle to simpliy the given expressions

1. Feb 19, 2012

### Johnyi

1. The problem statement, all variables and given/known data
Sin(sec^-1(sqrt(x^2+16)/4))

2. Relevant equations

3. The attempt at a solution
I did the math and ended up getting x^2-1 as the opposite, but the answers on the back of the book say other wise.

2. Feb 19, 2012

### alanlu

For future reference, trigonometry is usually precalculus material. Posting in the appropriate forum may be a good idea.

Assuming a is the adjacent side, b the opposite, and c the hypotenuse, you need to use

sec x = c / a (so arcsec c / a = x)
b2 = c2 - a2
sin x = b / c

Carefully resolve.

3. Feb 19, 2012

### Johnyi

My solution: b^2=(x^2+16/16) + 1

I dont know what to do from there!

4. Feb 19, 2012

### Staff: Mentor

This doesn't make any sense to me.

Draw a right triangle, with one acute angle labeled θ. Label the two sides and hypotenuse so that sec θ = √(x2 + 16)/4. With appropriate restrictions, this equation is equivalent to θ = sec-1[√(x2 + 16)/4].

After labeling the sides, find sinθ, and you're done.

5. Feb 19, 2012

### Johnyi

How do i get the opposite value?

6. Feb 19, 2012

### Staff: Mentor

It's a right triangle. If you know any two sides, you should be able to get the third.