Negative angle identities

$$ 1. \ \sin (−t)=−\sin (t) $$

$$ 2. \ \cos (−t)=\cos (t) $$

$$ 3. \ \tan (−t)=−\tan (t) $$

$$ 4. \ \cot (−t)=−\cot (t) $$

$$ 5. \ \sec (−t)=\sec (t) $$

$$ 6. \ \text{cosec} (−t)=−\text{cosec} (t) $$

Example 1:

What is \(\cos \left(-\frac {3\pi }{4}\right) \)?

Solution:

$$ \cos \left(-\frac {3\pi }{4} \right)= \cos \left(\frac {3\pi }{4}\right) = -\frac{\sqrt 2}{2} $$

Example 2:

What is \(\sin \left(-\frac {\pi }{2}\right) \)?

Solution:

$$ \sin \left(-\frac {\pi }{2} \right)=-\sin \left(\frac {\pi }{2} \right) =-1 $$