There's another identity involving sin 2θ:
.
Set sin 2θ equal to 5/13:
Cross multiply:
You have a quadratic with tan θ:
Thank god it's factorable:
There are two possibilities for tan θ:
Reject tan θ = 5 because you'll get an angle greater than 45°. So
Use the Pythagorean Theorem to get the hypotenuse (opposite = 1, adjacent = 5), and you'll get
.
Sine is defined as opposite over hypotenuse, so
.
I wish I would have known that definition of sin2a sometime yesterday...
If that particular definition derived from any others? the only formula for sin(2a) listed in my book is sin(2a) = 2cos(x)sin(x)...
This particular chapter seems to be horribly written.. many of the questions we are asked don't seemed to be covered in the book.. or require different methods than what we have been given..
I greatly appreciate the help.
This works as well, but it requires you to find so as to find . Now, can be found in exactly
the same as , so why not just find instead of finding so as to find ? In fact, finding
involves bit more of work than finding , as you will need to find the missing side of the triangle.