OS = 1.5 sin q<TSR
= q
ST
= 0.8 cos q
OT
= OS + ST
= 1.5 sin q
+ 0.8 cos q
= 1.7 sin (q
+ 28.07o)
apply
R-formula
(i)
OT is maximum when q
+ 28.07o = 90o recall
graph of sine function
q
= 61.9o
(ii)
1.7 sin (q
+ 28.07o) = 1.2
sin (q
+ 28.07o) = 1.2/1.7
q
+ 28.07o = 44.90o
q
= 16.8o
Description
of the procedure:
1st
step: Use addition formula on the numerator, factorise the denominator
2nd
step: sin90o = 0, cos2 B + sin2 B = 1
3rd
step: Split the fraction into two parts
4th
step: cos 2B is a common factor, can be eliminated. Use double angle formula
on sin 2B
5th
step: Use reciprocal functions.
Description
of the procedure:
1st
step: Covert cotangent to a quotient of cosine and sine
2nd
step: Cross multiplication
3rd
step: Eliminate common factor cos (A - B)
(i)
5 sin A cos B - 5 cos B sin A = 3 sin A cos B + 3 cos A sin B
Apply addition formula
2 sin A cos B = 8 cos A sin B
(2 sin A cos B) / (2 cos A sin B) = 4
tan A cot B = 4
(ii)
sin A = 4/5 --> tan A = 4/3
From
result of (i),
4/3 cot B = 4
cot B = 3
--->tan B = 1/3
Description
of the procedure:
1st
step: Regroup sin A + sin 7A, sin 3A + sin 5A, similar for cosine, and apply
factor formula
2nd
step: Factorise the numerator and denominatoe
3rd
step: Eliminate the common factor (cos 3A + cos A), tangent is the quotient of
sine and cosine.