Question

Why is -3sin(2t+30) equal to 3cos(2t+120)?

Answer 1

Look at the angles, 30 and 120.

Answer 2

One angle's sin is another angle's cos.

Answer 3

cos(A)=sin(90-A)

Simplifying RHS:-
3cos(2t+120)
=3sin(90-(2t+120) )
=3sin(-2t-30)
=3sin(-(2t+30) )
Now we know that , sin(-A)=-sinA
A=2t+30
Hence(proceeding from where we had left the simplification),
=-3sin(2t+30)
LHS=RHS

A lengthier process would be using the formulae: -

\[\sin (A+B)= \sin A \cos B+\cos A \sin B\]
\[\cos (A+B)=cosAcosB-sinAsinB\]
and using the known values of cos30 and sin30

Answer 4

As wio said we can also do that by looking at the quadrants