Verify the following coordinate transformations a rightarrow

Verify the following coordinate transformations {|a rightarrow|,L(a rightarrow)} = {2.1, -0.1} a rightarrow = (2.08951, -0.20965} {|a rightarrow|, L(a rightarrow)} = {4.7, -0.1} a rightarrow = (4.67652 -0.469217)

Solution

The modulus of |a| is 2.1 and the angle subtendd by it is -0.1 radians

horizontal component = 2.1cos(-0.1 radians) = 2.08951

vertical component = 2.1sin(-0.1 radians) = -0.20965

The modulus of |a| is 4.7 and the angle subtendd by it is -0.1 radians

horizontal component = 4.7cos(-0.1 radians) = 4.67652

vertical component = 4.7sin(-0.1 radians) = -0.469217