Consider the given expresssion,
[tex]\cos 34^{\circ}[/tex]It is observed that 34 degrees cannot be written as a sum or difference of any combination of known angles i.e. 0, 30, 45, 60, 90 degrees.
So the value can only be determined using a calculator.
There we get,
[tex]\cos 34^{\circ}=0.82904[/tex]But it is asked to round off to the nearest hundredth, so there should be only two digits past the decimal. Therefore, the values becomes,
[tex]\cos 34^{\circ}\approx0.83[/tex]Thus, the value of the expression is 0.83 approximately.