Please, Pleas help me with some trig here.

[thuper]

I have been grappling with these two problems and am ready to give up.

I managed to do several other trig problems but I'm stuck. I have no formulas and I haven't taken a math class (PreCal) in over a year.

Any help appreciated.


1. sec (arctan 2)

2. cos (2 arcsin (5/13))

Rules: Must be able to work on paper. So, no decimals just radians and fractions.

I don't necessarily want the answers, I want to know HOW to work them.

 

[misle]

This might help:
http://www.math.com/homeworkhelp/Trigonometry.html

I would try to break it down into Sin's and Cos's and work it out.

 

[Peetoeng]

Don't u have calculator?

Here are some clues:

arctan(x) = inverse tangent of x, look for inv and tan buttons on your calculator.

sec(x) = 1 / cos(x)

 

[DrPizza]

A calculator won't help later on when he gets sec(arctan(x+3))

here's a simple albeit non-perfect explanation (there are details that need to be filled in to make it complete, but this is all that's necessary for now to understand.)

arctan means "the angle whose tangent is..."


Sec(Arctan(2))
So, draw a right triangle. Pick one of the two acute angles to be "the angle". Label lengths on the other 2 sides such that the tangent of that angle =2. (since tangent is opposite over adjacent, the simplest way is to label the opposite side =2 and the adjacent side =1. Thus, the tangent of that angle is 2/1 = 2. Now, find the Sec of that angle. (it's not necessary to know the number of degrees in the angle). Pythag thm give's you sqrt(5) for the hypotenuse, secant = hypotenuse/adjacent, so the secant of the angles whose tangent is 2 = sqrt(5)/1. The only little details I'm leaving out concern domain/range for inverse functions... you need not be concerned by it at this time.