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'1' quadrant is (1,1) ; '-1' quadrant is (1,-1) ; what are quadrants (-1,1) and (-1,-1)?R=√10

a= 71.56

(√10) cos (2x - 71.57) = 2

The range in which we've to find the angle is 0<Θ<90 but we'll be needing to modify it.

0<Θ<90

multiply it by '2'.

0<2Θ<180

Subtract 71.56 from both the limits.

-71.56<2Θ<108.44

So according to this range, we'll be needing to find the angle in three quadrants; -1, 1 and 2.

(√10) cos (2Θ - 71.57) = 2

cos (2Θ - 71.57) = 0.6324

2Θ - 71.57 = 50.78

As the angle we've found is positive which in turn means that 'cos' is positive, we'll find the angle in the quadrant in which 'cos' is positive. 'Cos' is positive in the '-1' quadrant and the '1' quadrant; thus, it is quiet easy to find the value of Θ now.

'-1' quadrant:

2Θ - 71.57 = -50.78

2Θ = 20.79°

Θ = 10.4°

'1' quadrant:

2Θ - 71.57 = 50.78

2Θ = 122.35

Θ = 61.1°

Therefore, the 2 values of Θ are 10.4° and 61.1°.