Question

trig question:
use an identity to express 20sin⁡(πt/4-π/2) in terms of cos⁡〖πt/4〗

Answer 1

\[\large20\sin \left( \frac{ \pi t }{ 4 } - \frac \pi2 \right)\]

is this correct?

Answer 2

\[\sin(-\theta) =-\sin(-\theta)\]\[\sin \left( \frac \pi2 -\theta \right)= \cos (\theta)\]

Answer 3

\[\large{20\sin \left( \frac{ \pi t }{ 4 } - \frac \pi2 \right)\\ = -20\sin\left( \frac \pi2 -\frac{ \pi t }{ 4 }\right)\\=-20\cos\left(\frac{ \pi t }{ 4 }\right)}\]