Expert: Paul Klarreich - 5/3/2007

Question
I'm trying to solve 2.76=tan^2(45+x/2) but can't figure out how to get the x alone any ideas?

Answer
Questioner:   Lindsey
Category:  Advanced Math

Question:  I'm trying to solve 2.76=tan^2(45+x/2) but can't figure out how to get the x alone any ideas?
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Hi, Lindsey,

When you have:

some expression = trigfunction(something involving x),

Write:

thing involving x = arc trigfunction(expression)

[Arc trigfunction means inverse trigonometric function.  It's hard to write an exponent of -1 in this klutzy interface here.]

Now to your example:

2.76 = tan^2(45 + x/2)

First take the square root:  

tan(45 + x/2) = sqrt(2.76) = 1.661,  using my Windows calculator.

NOW we do that inverse function stuff:

1.661 = tan(45 + x/2)

45 + x/2 = arctan(1.661)

Now there is a problem with that 45.  It looks as if you mean 45 DEGREES, so I will assume that, although we all know that REAL MEN USE RADIAN MEASURE. (Real women, too.)

45 + x/2 = arctan(1.661)

I got  arctan(1.661) = 58.950084465933036940065884390795 degrees, on my Windows calculator:

0. Enter the 1.661
1. Set view to Scientific.
2. Click the degrees button.
3. Click Inv box.
4. Click tan

Make that 59 degrees.

45 + x/2 = 59

Solve for x:

x/2 = 14
x = 28.

That should do it.