Calculate the complex variables problem 7*cos(5*x + 5*pi/6) = _____________ *cos

Question

Calculate the complex variables problem

7*cos(5*x + 5*pi/6) =

_____________ *cos(5*x) + __________________*sin(5*x)

-4*cos(3*x) - 0*sin(3*x) =

_____________ * cos(3*x + ________________ )

You must enter a half as 1/2 and not 0.5. You must enter 3*sqrt(2)/2 and not 2.121 or 3sqrt(2)/2. You must also choose values for all angles between -pi and pi and the amplitudes in problems 2, 3, and 4 should be positive

7*cos(5*x + 5*pi/6) =

_____________ *cos(5*x) + __________________*sin(5*x)

-4*cos(3*x) - 0*sin(3*x) =

_____________ * cos(3*x + ________________ )

Explanation / Answer

7*cos(5*x + 5*pi/6) = 7*cos(5*x)*cos(5*pi/6) - 7*sin(5*x)*sin(5*pi/6)

= -7*sqrt(3)*cos(5*x)/2 - 7*sin(5*x)/2

-4*cos(3*x) - 0*sin(3*x) = 4*cos(3*x)*cos(pi) - 4*sin(3*x)*sin(pi)

= 4*cos(3*x + pi)

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