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
[tex] \sqrt{\frac{1+cos}{2} } [/tex]
By following the formula, cos=3/5 then:
[tex] \sqrt{ \frac{1- \frac{3}{5} }{2} } [/tex] Multiply everything (inside the square [tex] \sqrt{ \frac{5+3}{10} } [/tex] root) by 5
[tex] \frac{2 \sqrt{2} }{ \sqrt{10} } [/tex]
[tex] \frac{2 \sqrt{20} }{10} [/tex] Then just simplify
[tex] \frac{ \sqrt{20} }{5} [/tex] The answer is Square root of 20 over 5
