Find the Exact Value cos(225 degrees )

$\cos (225 °)$

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.

$- \cos (45)$

The exact value of $\cos (45)$ is $\frac{\sqrt{2}}{2}$ .

$- \frac{\sqrt{2}}{2}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{2}}{2}$

Decimal Form:

$- 0.70710678 \dots$

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