What is the value of $ sin(15^circ) $ using the unit circle?
Answer 1
Chloe Evans
To find the value of $ \sin(15^\circ) $ using the unit circle, we use the angle addition formula:
$ \sin(a + b) = \sin(a) \cos(b) + \cos(a)\sin(b) $
Here, let $ a = 45^\circ $ and $ b = -30^\circ $. Then,
$ \sin(45^\circ – 30^\circ) = \sin(45^\circ)\cos(30^\circ) + \cos(45^\circ)\sin(30^\circ) $
Substituting the values, we get:
$ \sin(15^\circ) = \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{2}}{2} \cdot \frac{1}{2} $
Simplify the expression:
$ \sin(15^\circ) = \frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{4} $
Combine the fractions:
$ \sin(15^\circ) = \frac{\sqrt{6} + \sqrt{2}}{4} $
Answer 2
Ella Lewis
To find the value of $ sin(15^circ) $ using the unit circle, we use the angle addition formula:
$ sin(a + b) = sin(a) cos(b) + cos(a)sin(b) $
Here, let $ a = 45^circ $ and $ b = -30^circ $. Then,
$ sin(45^circ – 30^circ) = sin(45^circ)cos(30^circ) + cos(45^circ)sin(30^circ) $
Substituting the values, we get:
$ sin(15^circ) = frac{sqrt{2}}{2} cdot frac{sqrt{3}}{2} + frac{sqrt{2}}{2} cdot frac{1}{2} $
Simplify the expression:
$ sin(15^circ) = frac{sqrt{6}}{4} + frac{sqrt{2}}{4} $
Answer 3
Christopher Garcia
To find the value of $ sin(15^circ) $ using the unit circle, we use the angle addition formula:
$ sin(a + b) = sin(a) cos(b) + cos(a)sin(b) $
Here, let $ a = 45^circ $ and $ b = -30^circ $. Then,
$ sin(15^circ) = frac{sqrt{6}}{4} + frac{sqrt{2}}{4} $
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