Question 1040970
<pre>
There are two methods, right triangle and identities.

Either method you use, you will have to go by what quadrants are 
possible for theta.  If the tangent is a positive number, theta
is either in QI or QIII.  If the tangent is negative, theta is in
QII or QIV.

One way is to make a triangle like this in whatever quadrant
theta is in.  I have the triangle drawn below in the first
quadrant, but you can draw it in whichever quadrant theta is in.

{{{drawing(200,100,-.5,2,-.5,1.5,line(-3,0,3,0),line(0,-3,0,3), line(0,0,1.5,1),line(1.5,0,1.5,1),locate(.4,.3,theta), locate(1.53,.62,tan(theta)),locate(.77,0.05,1),locate(.75,.85,H) )}}} 

Since you know the tangent, you can use the Pythagorean theorem
to find the hypotenuse.  Then the sine is opposite/hypotenuse,
and the cosine is adjacent/hypotenuse.

Then add the sine and the cosine.
  
-------------------------------------

Another way is to use identities:

Use {{{1+tan^2(theta)=sec^2(theta)}}} to find {{{sec^2(theta)}}} and {{{sec(theta)}}}.

Then use {{{cos(theta)=1/sec(theta)}}} to find {{{cos(theta)}}}.

Then use {{{sin^2(theta)+cos^2(theta)=1}}} to find {{{sin(theta)}}}.

Then add the sine and the cosine.

Edwin</pre>