Find the Exact Value cos(120 degrees )+cos(45 degrees )

$\cos (120 °) + \cos (45 °)$

Step 1

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 second quadrant.

$- \cos (60) + \cos (45 °)$

Step 2

The exact value of $\cos (60)$ is $\frac{1}{2}$ .

$- \frac{1}{2} + \cos (45 °)$

Step 3

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

$- \frac{1}{2} + \frac{\sqrt{2}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2} + \frac{\sqrt{2}}{2}$

Decimal Form:

$0.20710678 \dots$

Find the Exact Value cos(120 degrees )+cos(45 degrees )

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