How do you find the intersections points of $y = - cos x$ $y=-cosx$ and $y = sin x$ $y=sinx$ ?

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Answer 1 · 2016-11-11T23:01:37

Please see the explanation.

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

$- cos (x) = sin (x)$ $-cos(x) = sin(x)$

Divide both sides by $cos (x)$ $cos(x)$ :

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

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

$tan (x) = - 1$ $tan(x) = -1$

This occurs at:

$x = \frac{3 π}{4} + n π$ $x = (3pi)/4 + npi$

where n is any integer:

$n = ...,-3,-2,-1,0,1,2,3,...$

The y value is $sqrt(2)/2$ , if n is even and $-sqrt(2)/2$ , if n is odd.

Here is a graph that shows a few intersection points:
purple is y = -cos(x), orange is y = sin(x)

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