URGENT Question

In the unit circle we find by using the periphery angle:

$\tan{( \frac{\theta}{2} ) } = \frac{ \sin{( \theta ) }}{ 1+\cos{(\theta ) }}$

49.

$\begin{array}{rcll} \tan{( \frac{\theta}{2} ) } &=& \frac{ \sin{( \theta ) }}{ 1+\cos{(\theta ) }} \qquad \sin{( \theta ) } = \frac35 \qquad \cos{( \theta ) } = \frac45 \\ \tan{( \frac{\theta}{2} ) } &=& \frac{ \frac35 }{ 1+\frac45 } \\ \tan{( \frac{\theta}{2} ) } &=& \frac35 \cdot \frac{ 1 }{ 1+\frac45 } \\ \tan{( \frac{\theta}{2} ) } &=& \frac35 \cdot \frac{ 1 }{ \frac{5+4}{5} } \\ \tan{( \frac{\theta}{2} ) } &=& \frac35 \cdot \frac{ 5 }{ 9 } \\ \tan{( \frac{\theta}{2} ) } &=& \frac39 \\ \tan{( \frac{\theta}{2} ) } &=& \frac13 \\ \end{array}$

tan (theta/ 2)  = sqrt ( [1 - cos(theta)]  / [ 1 + cos(theta)] )  = sqrt ( [ 1 - (4/5)] / [ 1 + (4/5)])  =

sqrt ( [1/5] / [ 9/5] )  =  sqrt [ 1/9]   = 1/3