# cos(-13pi/4)

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`cos(-(13pi)/4)`

According to basic trignometry and signs in quadrants,

`cos(-A) = cos(A)`

Therefore,

`cos(-(13pi)/4) = cos((13pi)/4)`

I can rewrite the above expression as,

`cos(-(13pi)/4) = cos((8pi+5pi)/4)`

`cos(-(13pi)/4) = cos(2pi+(5pi)/4)`

We know, cos(2pi+A) = cos(A)

Therefore,

`cos(-(13pi)/4) = cos((5pi)/4)`

`cos(-(13pi)/4) = cos(pi+pi/4)`

We know,

`cos(pi+A) = -cos(A)`

Therefore,

`cos(-(13pi)/4) = -cos(pi/4)`

**Therefore **`cos(-(13pi)/4) = -1/sqrt(2)`

**Sources:**

cos(-13pi/4)

-13/4 = 3 and 1/4

Orienting yourself on the unit circle, -13pi / 4 is the same as going around the circle three times and then all the way to pi/4

so this is actually equal to cos(-pi/4) which is equal to -cos(pi/4) = -sqrt(2)/2