How do you find the intersections points of y=-cosx and y=sinx?

Nov 11, 2016

Explanation:

Because $y = y$ at the point of intersection, we can write the following equation:

$- \cos \left(x\right) = \sin \left(x\right)$

Divide both sides by $\cos \left(x\right)$:

$- 1 = \sin \frac{x}{\cos} \left(x\right)$

Use the identity $\tan \left(x\right) = \sin \frac{x}{\cos} \left(x\right)$:

$\tan \left(x\right) = - 1$

This occurs at:

$x = \frac{3 \pi}{4} + n \pi$

where n is any integer:

$n = \ldots , - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , \ldots$

The y value is $\frac{\sqrt{2}}{2}$, if n is even and $- \frac{\sqrt{2}}{2}$, if n is odd.

Here is a graph that shows a few intersection points: