Natural log and trig exponents

**chris520** · March 7th 2011, 04:16 AM

I'm h

**Prove It** · March 7th 2011, 04:54 AM

Is this what you're trying to solve?

$\displaystyle \left(\frac{81}{256}\right)^{\sin^2{\theta}} + \left(\frac{81}{256}\right)^{\cos^2{\theta}} = \frac{75}{64}$ ?

If so...

$\displaystyle \left(\frac{81}{256}\right)^{1 - \cos^2{\theta}} + \left(\frac{81}{256}\right)^{\cos^2{\theta}} = \frac{75}{64}$

$\displaystyle \frac{\frac{81}{256}}{\left(\frac{81}{256}\right)^ {\cos^2{\theta}}} + \left(\frac{81}{256}\right)^{\cos^2{\theta}} = \frac{75}{64}$

$\displaystyle \frac{81}{256} + \left[\left(\frac{81}{256}\right)^{\cos^2{\theta}}\right]^2 = \frac{75}{64}\left(\frac{81}{256}\right)^{\cos^2{\ theta}}$

$\displaystyle \left[\left(\frac{81}{256}\right)^{\cos^2{\theta}}\right]^2 - \frac{75}{64}\left(\frac{81}{256}\right)^{\cos^2{\ theta}} + \frac{81}{256} = 0$ .

Now let $\displaystyle x = \left(\frac{81}{256}\right)^{\cos^2{\theta}}$ so that we can write the equation as

$\displaystyle x^2 - \frac{75}{64}x + \frac{81}{256} = 0$

which is a quadratic equation you can solve for $\displaystyle x$ , the solution of which you can use to solve for $\displaystyle \theta$ .

**chris520** · March 7th 2011, 02:41 PM

j

Thread: Natural log and trig exponents

LinkBack

Thread Tools

Display

Natural log and trig exponents

Similar Math Help Forum Discussions

Derivative of trig functions under the natural log

Even More Natural Log Problems With trig =D

[SOLVED] Trig functions, exponents of trig functions, and tring stunt variables

Natural Exponents and Integration

logs and exponents of natural base

Search Tags