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Question
Find the exact value of the expression.
sin (15 degrees)
Solution
VerifiedAnswered 2 years ago
Answered 2 years ago
Step 1
1 of 2Notice that $15\text{\textdegree}=45\text{\textdegree}60\text{\textdegree}$, so
$\sin (15\text{\textdegree})=\sin(45\text{\textdegree}60\text{\textdegree})$
Apply formula (2):
$\sin(45\text{\textdegree}60\text{\textdegree})=\\\\ =\sin 45\text{\textdegree}\cos 60\text{\textdegree}\cos 45\text{\textdegree}\sin 60\text{\textdegree}=\\\\ =\dfrac{\sqrt 2}{2}\cdot \dfrac{1}{2}\dfrac{\sqrt 2}{2}\cdot \dfrac{\sqrt 3}{2}=\\\\ =\dfrac{\sqrt 2}{4}\dfrac{\sqrt 6}{4}=\\\\ =\dfrac{\sqrt 2\sqrt 6}{4}$
Sum and Difference Formulas for Cosine and Sine:

$\cos(a\pm b)=\cos a\cos b\mp \sin a\sin b$

$\sin (a\pm b)=\sin a\cos b\pm \cos a\sin b$
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