# (R + RCos (2,57 (20)) = 12), How to solve for R?

Mar 29, 2016

This solution is based on $\cos \left(2.57 \times 20\right)$
$R \approx 7.390$ to 3 decimal places
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$R = \frac{12}{1 + \cos \left(2.5720\right)} \approx 6.003$ to 3 decimal places

#### Explanation:

Given: $R + R \cos \left(2.57 \left(20\right)\right) = 12$

Factor out the R giving

R(1+cos(2.57(20))=12

Divide both sides by (1+cos(2.57(20)) giving

$R \times \frac{1 + \cos \left(2.57 \left(20\right)\right)}{1 + \cos \left(2.57 \left(20\right)\right)} = \frac{12}{1 + \cos \left(2.57 \left(20\right)\right)}$

But $\frac{1 + \cos \left(2.57 \left(20\right)\right)}{1 + \cos \left(2.57 \left(20\right)\right)} = 1$ giving

$R = \frac{12}{1 + \cos \left(2.57 \left(20\right)\right)}$

$R \approx 7.390$ to 3 decimal places

This solution is based on $\cos \left(2.57 \times 20\right)$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Or, if you meant:
$R = \frac{12}{1 + \cos \left(2.5720\right)}$

$R = 6.003$ to 3 decimal places