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Question

# Find the exact value of the expression.sin (-15 degrees)

Solution

Verified
Step 1
1 of 2

Notice 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:

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

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

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