Question

How do I solve these equations

Answer 1

You need to know the properties of each function.
Tan is opposite (y) over adjacent (x).  Sin>0 means that sin is positive, therefore, it is located on either quadrant 1 or 2. Tan=4/3  so it is located in quadrant 1.
The side of the triangle must be Adjacent=3  opposite=4 and hypotenuse=5
Now, you are asked to find the half angle of Cos which is 
$\sqrt{\frac{1+cos}{2} }$
By following the formula, cos=3/5 then:
$\sqrt{ \frac{1- \frac{3}{5} }{2} }$    Multiply everything (inside the square          $\sqrt{ \frac{5+3}{10} }$                  root) by 5
$\frac{2 \sqrt{2} }{ \sqrt{10} }$
$\frac{2 \sqrt{20} }{10}$                Then just simplify
$\frac{ \sqrt{20} }{5}$      The answer is Square root of 20 over 5