This is a list of equations in my book:
$$\sin(90-\theta)=\cos\theta$$ $$\cos(90-\theta)= \sin\theta$$ $$\tan(90-\theta)=\cot\theta$$
$$\sin(180-\theta)=\sin\theta$$ $$\cos(180-\theta)= -\cos\theta$$ $$\tan(180-\theta)=-\tan\theta$$
The list goes on and on $(90+\theta)$, $(180+\theta)$ etc
I can find these equations by drawing a unit circle and then figure the above but in our exams, we need to answer the questions related to these equations very quickly.
the value of $\cos(675)$
The answer is $\sin(45)$... I need to answer such a question very quickly. So, could someone please tell me how I could remember all these equations and apply them without using unit circles which take a long time to do.