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bixtya [17]
3 years ago
10

Find the exact value of sin 165º.

Mathematics
2 answers:
ra1l [238]3 years ago
8 0

Answer:0.2588

Step-by-step explanation:

lisabon 2012 [21]3 years ago
4 0

Answer:

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

Step-by-step explanation:

Using the sine addition formula

sin(a + b) = sinacosb + cosasinb

and the exact values

sin45° = cos45° = \frac{\sqrt{2} }{2} , sin60° = \frac{\sqrt{3} }{2} , cos60° = \frac{1}{2}

Given

sin165°

Note that 165° = (120 + 45)°, thus

= sin(120 + 45)°

= sin120°cos45° + cos120°sin45°

= sin60°cos45° - cos60°sin45°

= ( \frac{\sqrt{3} }{2} × \frac{\sqrt{2} }{2} ) - ( \frac{1}{2} × \frac{\sqrt{2} }{2} )

= \frac{\sqrt{6} }{4} - \frac{\sqrt{2} }{4}

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

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