Phasor to Time Domain Math

[Mark Zhu]

Homework Statement

See image attachment

Relevant Equations

I(d, t) = Re[I (d) e ^ jωt]

This is a problem about converting from the phasor to time domain. I am having trouble following the math that the textbook is doing.
I was thinking the final answer should be:
i(d, t) = 0.20 cos(ωt + βd + 159◦) - 0.091 cos(ωt − βd + 185.6◦)
emphasize the minus 0.091 instead of plus 0.091 as shown in the image attachment and textbook.
Am I missing something here? Thank you.

 

[Charles Link]

Looks like it should be a minus sign. My arithmetic also gives me $-.090$.

 

[Mark Zhu]

Thank you, I also consulted with someone else and we thought the textbook had made an error as well.