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Without using calculator find the value of sin $105^{0}$

written 5.6 years ago by teamques10 ★ 69k

modified 3.0 years ago by pedsangini276 • 4.8k

engineering mathematics

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1 Answer

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written 5.6 years ago by teamques10 ★ 69k

•   modified 5.6 years ago

Solution:

$=sin \left(105^{\circ}\right)$

$=\sin \left(60^{\circ}+45^{\circ}\right)$

$=\sin 60^{\circ} \cos 45^{\circ}+\cos 60^{\circ} \sin 45^{\circ}$

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

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

OR 0.9659

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