What is -cos(t) equivalent to in terms of cos(t) I want to know if,

$-\cos(t) = \cos(t+180)$

or

$-\cos(t) = \cos(t-180)$

Please guide me. Thanks
 A: Yes, both are true: $$-\cos (t) = \cos (t \pm 180^\circ)\quad\text{ or in radians, }\;\;-\cos(t) = (t \pm \pi)$$
Note that $$t + 180^\circ - (t - 180^\circ) = 360^\circ$$
See this link for similar trigonometric "shifts"
In the same Wikipedia article, you'll find a handy diagram with ordered pairs $(\cos x, \sin x)$ for angle x measured in radians, as they appear cycle the unit circle:

A: Both answers are correct. Note that $t+180^\circ$ and $t-180^\circ$ differ by $360^\circ$, so they have the same cosine (and sine).
Let's verify that $\cos(t+180^\circ)=-\cos t$. If you rotate a point $(x,y)$ around the origin  through $180^\circ$, both the $x$ and $y$-coordinate of the point change sign. It follows that $\cos(t+180^\circ)=-\cos t$ and $\sin(t+180^\circ)=-\sin t$. 
A: As a separate verification, you can use the "angle-addition" formula for cosine:
$$\cos (t \pm 180^{\circ})  = \cos t \cdot \cos (\pm 180^{\circ}) \mp \sin t \cdot \sin (\pm 180^{\circ})$$
$$= (\cos t) \cdot [-1] \mp (\sin t) \cdot 0  = -\cos t .$$
You can reconstruct a lot of trig identities for complementary angles, supplementary angles, etc. with the angle-addition rules for sine, cosine, and tangent.
