How do you evaluate $sin (\frac{π}{4}) cos (\frac{π}{6}) - sin (\frac{π}{6}) cos (\frac{π}{4})$ $sin (pi/4) cos (pi/6) - sin (pi/6) cos (pi/4)$ ?

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How do you evaluate $sin (\frac{π}{4}) cos (\frac{π}{6}) - sin (\frac{π}{6}) cos (\frac{π}{4})$ $sin (pi/4) cos (pi/6) - sin (pi/6) cos (pi/4)$ ?

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Answer 1 · 2016-04-05T13:29:51

$0.26$ $0.26$

Explanation:

The most straightforward way to do it (in my opinion) is to substitute $π = 180^{o}$ $pi = 180^o$ and use degrees.

Therefore,

$sin (\frac{π}{4}) = sin (45) = \frac{\sqrt{2}}{2}$ $sin(pi/4) = sin(45) = sqrt2/2$
$cos (\frac{π}{6}) = cos (30) = \frac{\sqrt{3}}{2}$ $cos(pi/6) = cos(30) = sqrt3/2$
$sin (\frac{π}{6}) = sin (30) = \frac{1}{2}$ $sin(pi/6) = sin(30) = 1/2$
$cos (\frac{π}{4}) = cos (45) = \frac{\sqrt{2}}{2}$ $cos(pi/4) = cos(45) = sqrt2/2$

Put these into the original equation, and you get

$\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} - \frac{1}{2} \cdot \frac{\sqrt{2}}{2}$ $sqrt2/2*sqrt3/2 - 1/2*sqrt2/2$

Rearranging these become

$\frac{\sqrt{2}}{2} (\frac{\sqrt{3} - 1}{2}) = \frac{\sqrt{6} - \sqrt{2}}{4}$ $sqrt2/2((sqrt3-1)/2) = (sqrt6-sqrt2)/4$

If you want this in a decimal form, use a calculator or a savant

$\approx 0.26$ $approx 0.26$

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How do you evaluate $sin (\frac{π}{4}) cos (\frac{π}{6}) - sin (\frac{π}{6}) cos (\frac{π}{4})$ $sin (pi/4) cos (pi/6) - sin (pi/6) cos (pi/4)$ ?

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Explanation:

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