Originally Posted by
ticbol sinX = sin(X +2)
Normally, it would be X = X +2.
But that leads to nowhere.
So do it by expansion:
sinX = sinXcos(2) +cosXsin(2)
sinX -sinXcos(2) = cosXsin(2)
sinX(1 -cos(2)) = cosXsin(2)
Divide both sides by cosX,
tanX(1 -cos(2)) = sin(2)
tanX = sin(2) / (1 -cos(2))
Using the calculator,
tanX = 0.642096 -------------positive tan, so X is in the 1st or 3rd quadrants.
X = arctan(0.642096) = 0.570796 radian
In the 1st quadrant,
X = 0.570796 radian -----------answer.
In the 3rd quadrant,
X = pi +0.570796 = 3.712389 radians ---------answer.
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You should be able to solve the second equation now.
You should find that X is in the 2nd or 4th quadrants,
and X = 2.641593 or 5.783185 radians.