Why $\cos(-\theta)$ gives positive values while in case of sine it is negative?
I mean
$\cos(-\theta) = +\cos(\theta)$
$\sin(-\theta) = -\sin(\theta)$
$\tan(-\theta) = -\tan(\theta)$
and please explain General Angles in simple worlds?
trigonometry
Why $\cos(-\theta)$ gives positive values while in case of sine it is negative?
I mean
$\cos(-\theta) = +\cos(\theta)$
$\sin(-\theta) = -\sin(\theta)$
$\tan(-\theta) = -\tan(\theta)$
and please explain General Angles in simple worlds?
Best Answer
Changing the sign of $\theta$ corresponds to going around in the other direction. Because $\theta$ is measured from the positive $x$-axis, all this does is to flip the endpoint over the $x$-axis, as shown below.
Since cosine is the $x$-component of $P$, and sine is the $y$ component, flipping over the $x$-axis will negate $\sin \theta$, but not $\cos \theta$. Hopefully this makes it clear why sine and cosine behave the way they do.
With tangent, just recall that $\tan \theta = \frac{\sin \theta }{\cos \theta }$, and since only one part of the fraction gets a $-$ sign, the tangent gets one as well.