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.