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How do you evaluate sin (165)?
Sub Grade: 10

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\frac{1}{4} (\sqrt{6} - \sqrt{2)}

\frac{1}{4} (2 - \sqrt{6)}

\frac{1}{4} (3 - \sqrt{2)}

\frac{1}{4} (\sqrt{2} - \sqrt{3)}

answer is A.

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Detailed Solution

Some things we will use:
sin(Ө)=sin (180°-Ө)
sin (𝛂-𝛃)=sin𝛂 cos𝛃 -sin𝛃 cos𝛂
sin 45°=cos 45°=

\frac{\sqrt 2}{2}

Sin 30° =

\frac{1}{2}

Hence we find
Sin 165° =sin (180°-165°)
=sin 15°
Sin (45°-30°)
=sin 45° cos30°-sin 30° cos 45°
=

\frac{\sqrt 2}{2} \frac{\sqrt 3}{2}

\frac{1}{2}

\frac{\sqrt 2}{2}

\frac{1}{4}

(√6-√2)
Type Exam: CBSE

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