the clock code
Send Clowns and jsf are both right. The mathematics of applying sine and cosine become more complicated as you change heading to compensate for wind because this heading change causes the amount of drift that you are esposed to to change. jsf is also right for a practical application of the clock code but what is that?
Draw yourself a circle( a clockface) and divide it into four quaters.
At the 3oclock position mark 15 (15 minutes past the hour)
At the 6oclock position mark 30 (30 minutes past the hour)
At the 9oclock position mark 45 (45 minutes past the hour)
At the 12oclock position mark 60 (60 minutes past the hour)
Sine 15 is about .2588 or approx 0.25 so mark 1/4 at the 3 oclock position
Sine 30 is 1/2 so mark this at the 6 oclock position
Sine 45 is .707 which can be rounded up to 3/4 for the 9 oclock position.
Sine 60 is 0.866 so rounf this up to 1.0 and place in the 12 oclock position.
So for crosswind calculations you can now memorise this little chart.
If the wind is 15 degrees off the nose then you apply 1/4 of the wind component as a crosswind. So for a twenty knot wind this would equate to a 5 knot crosswind.
At 60 knots you would apply 5 degrees of drift ,at 120 knots you wouls apply half that etc.
If the wind is for instance 20 degrees off you can intepolate your chart and say that 20 mins past the hour is 1/3. Sine 20 is very nearly equal to 1/3.
Once the angle >60 then 0.866 or greater is so nearly 1 then just apply the full wind component.
These rules of thumb dont give you precise answers but if you can fly to these rule of thumb tolorences your aerolpane will be on track.
Cosine???
Well cosine 15 is 0.9659.
Cosine 30 is 0.866
Cosine 45 is 0.707
Cosine 60 is 1/2
Use them for head/tail wind calcs
Up to 30 degrees 0.866 just apply the full head or tail component to calucate ground speed.
At 60 degrees off the nose you have a half head/tail component.
Rule of thumb. Forget memorising cosines
Take the crosswind angle away from 90 and use this figure to re-enter your memorised clockcode and apply the relevant fraction.
From your intial example 90-60 =30 (sine 30=1/2) therfore apply 1/2 the headwind component to your airspeed to calculate groundspeed ie; 105 knots.
Of course if you want to be clever you are now heading 075 and therefore the crosswind is now only 45 degrees and your headwind exposure has increaed to 45 degrees ie 3/4 so ground speed closer to 98 knots.
Hope this helps