Question 575442
You need a trigonometric identity. Either you find trigonometric identities from some source, or you deduce the ones you do not remember from the ones you do remember. You can search for "trigonometric identities" on the internet and will find them in many sites, including Wikipedia.
I do not believe in memorizing, but unfortunately I have not been able to convince teachers.
I remember the fact that
{{{cos^2(theta)+sin^2(theta)=1}}} --> {{{sin(theta)=sqrt(1-cos^2(theta))}}} for QI and QII (For angles in the third and fourth quadrants I have to put a minus sign in front of the square root, but in QI and QII, sine is positive).
So substituting into the definition of tangent,
{{{tan(theta)=sin(theta)/cos(theta)}}}, which I also remember, I get
{{{tan(theta)=sqrt(1-cos^2(theta))/cos(theta)}}}
Now that I found my trigonometric identity, it's just plug and chug:
{{{tan(theta)=sqrt(1-(-0.99619470)^2)/(-0.99619470)=-0.087489}}}
I would not write more digits because the next digit varies if I use -0.99619471 or -0.99619469 for {{{cos(theta)}}}