First slide

Trigonometric Identities

Question

If $θ = \frac{11 π}{6},$ then $\cos θ + \sin θ =$

Moderate

A

$\frac{\sqrt{3} + 1}{\sqrt{2}}$
B

$\frac{\sqrt{3} - 1}{\sqrt{2}}$
C

$\frac{\sqrt{3} - 1}{2}$
D

$\frac{\sqrt{3} + 1}{2}$

Solution

$\cos \frac{11 π}{6} + \sin \frac{11 π}{6} = \cos (2 π - \frac{π}{6}) + \sin (2 π - \frac{π}{6}) = \cos \frac{π}{6} - \sin \frac{π}{6} = \frac{\sqrt{3} - 1}{2}$

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