Find the Exact Value sin(-pi/3)+cos((5pi)/4)

$\sin (- \frac{π}{3}) + \cos (\frac{5 π}{4})$

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\sin (\frac{5 π}{3}) + \cos (\frac{5 π}{4})$

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

$- \sin (\frac{π}{3}) + \cos (\frac{5 π}{4})$

The exact value of $\sin (\frac{π}{3})$ is $\frac{\sqrt{3}}{2}$ .

$- \frac{\sqrt{3}}{2} + \cos (\frac{5 π}{4})$

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.

$- \frac{\sqrt{3}}{2} - \cos (\frac{π}{4})$

The exact value of $\cos (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$- \frac{\sqrt{3}}{2} - \frac{\sqrt{2}}{2}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{3}}{2} - \frac{\sqrt{2}}{2}$

Decimal Form:

$- 1.57313218 \dots$

Find the Exact Value sin(-pi/3)+cos((5pi)/4)

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