Question 978130
Your answer is right, understanding that you are expressing the angle in radians.
Since the multiple choice answers have the angle measured in degrees,
none of the options given looks like a match.
 
In this case, no calculations are needed to pick the right answer.
Because the real part and the imaginary part of {{{6 + 8i}}} are positive numbers,
you know that the sine and cosine must be positive,
meaning that the angle must be between {{{0^o}}} and {{{90^o}}} ,
so the answer is obviously {{{highlight(C)}}} .
 
If we had to calculate, we would calculate
{{{sqrt(6^2+8^2)=sqrt(36+64)=sqrt(100)=10}}} for the modulus,
and we would pick an angle {{{theta}}} such that
{{{system(tan(theta)=8/6=4/3,"and",0^o<=theta<360^o)}}}
Using a cheap scientific calculator in degree mode, I get that the angle is approximately {{{53.13010235^o}}} , which rounds to {{{53.1^o}}} .
If I had not found that calculator quickly enough,
I would have used Excel that would give me the {{{0.92729522}}} (radian) answer you posted.
Them, I would have converted to degrees by multiplying times {{{180^o/pi}}} ;
{{{0.92729522*180^o/pi=53.1301}}} (rounded).