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What is the exact value of sin (165 degrees)

What Is The Exact Value Of Sin 165 Degrees class=

Sagot :

Answer:

A

Step-by-step explanation:

Think of a value on the unit circle that is double of 165.

330 is that so we can use the double Angle Identity

[tex] \sin( \frac{ \alpha }{2} ) = \sqrt{ \frac{1 - \cos( \alpha ) }{2} } [/tex]

Alpha is 330

so

[tex] \sin(165) = \sqrt{ \frac{1 - \cos(330) }{2} } [/tex]

[tex] \sin(165) = \sqrt{ \frac{1 - \frac{ \sqrt{3} }{2} }{2} } [/tex]

[tex] \sin(165) = \sqrt{ \frac{ \frac{2 - \sqrt{3} }{2} }{2} } [/tex]

[tex] \sin(165) = \sqrt{ \frac{2 - \sqrt{3} }{4} } [/tex]

[tex] \sin(165) = \frac{ \sqrt{2 - \sqrt{3} } }{2} [/tex]